Articoli di riviste sul tema "Lagrange FE"

Mechanical systems, called by use, mechanical (ρ, η)-systems, Lagrange mechanical (ρ, η)-systems or Finsler mechanical (ρ, η)-systems, are presented. The canonical (ρ, η)-semi(spray) associated to a mechanical (ρ, η)-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical (ρ, η)-systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the (ρ, η)-semispray associated to a regular Lagrangian L and external force Fe and we derive the equations of Euler–Lagrange type. So, a new solution for the Weinstein's problem in the general framework of generalized Lie algebroids is presented.

This US-FE-LSPIM QUAD4 element is formed by using two different sets of shape functions for the trial and test functions, viz. sets of FE-LSPIM QUAD4 element shape functions and sets of classical isoparametric shape functions. For some test problems, the US-FE-LSPIM QUAD4 element has good accuracy. And by compared with FE-LSPIM QUAD4 element, the proposed element does not need to use Penalty method or Lagrange multiplier method to ensure fulfilment of exact essential boundary condition along the entire length of the edge. This paper further studies the performance of US-FE-LSPIM QUAD4 element on mesh distortion. Numerical test examples show that the element exhibits high precisions even under the mesh distortions. The US-FE-LSPIM QUAD4 element displays good tolerance to the mesh distortions

The aim of this paper is the comparison of different material models for the simulation of fluid impact on a cask for transport of radioactive liquid material. Simulated is a 9 m drop test performed according to International Atomic Energy Agency regulations. In order to reduce computational time, proposed is to model the transported fluid as a hypothetic linearly elastic material. This enables us to use less time demanding FE explicit dynamic analysis based on Lagrange formulation only instead of combination of Lagrange and Euler formulations. Compared are the results obtained for three elastic material and three fluid models based on different equations of state.

Purpose The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward with respect to the elementary structure of finite element (FE) codes. This often discourages industrial engineers from adopting isogeometric capabilities in their well-established simulation environment. Design/methodology/approach Based on the concept of Bézier and Lagrange extractions, a novel method is proposed to implement IGA from an existing industrial FE code with the aim of bringing human implementation effort to the minimal possible level (only using standard input-output of finite element analysis (FEA) codes, avoid code-dependent subroutines implementation). An approximate global link to go from Lagrange polynomials to non-uniform-rational-B-splines functions is formulated, which enables the whole FE routines to be untouched during the implementation. Findings As a result, only the linear system resolution step is bypassed: the resolution is performed in an external script after projecting the FE system onto the reduced, more regular and isogeometric basis. The novel procedure is successfully validated through different numerical experiments involving linear and nonlinear isogeometric analyses using the standard input/output of the industrial FE software Code_Aster. Originality/value A non-invasive implementation of IGA into FEA software is proposed. The whole FE routines are untouched during the novel implementation procedure; a focus is made on the IGA solution of nonlinear problems from existing FEA software; technical details on the approach are provided by means of illustrative examples and step-by-step implementation; the methodology is evaluated on a range of two- and three-dimensional elasticity and elastoplasticity benchmarks solved using the commercial software Code_Aster.

This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom.

In dieser Arbeit werden geschichtete Platten unter statischer Belastung betrachtet. Es wird ein Mehrfeldfunktional vorgeschlagen, dessen zugehörige Euler–Lagrange–Gleichungen neben dem Kräfte– und Momentengleichgewicht der Schnittgrößen lokale Gleichgewichtsbeziehungen in Spannungen liefert. Innerhalb eines finiten Plattenelements mit vier Knoten werden die Verwölbungen mit schichtweisen kubischen Ansatzfunktionen interpoliert. Dies hat zur Folge, dass die interlaminaren Schubspannungen automatisch kontinuierlich und die Spannungsrandbedingungen exakt erfüllt sind. Elimination der Wölb– und Lagrangeparameter auf Elementebene führt zu einem gemischt–hybriden Plattenelement mit fünf Freiheitsgraden an den Knoten. Damit können übliche Verschiebungsrandbedingungen angesetzt werden.

This paper proposed a finite element formulation to analysis the vibration of couple-stress continuum. A four-node discrete couple-stress element relaxed the requirement of C1 continuity is developed. This element is modified by a bubble function, based on the classical four-ode Lagrange element. The element includes the internal bending constants and the internal initial moment of rotation. Numerical examples show that the present FE scheme is accurate for the eigenvalue analysis of couple-stress continuum structures, especially for the low order frequency analysis.

This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids using classical Lagrangemultipliers. These methods tend to generate strongly coupled systems that require a deep knowledgeof the discretization characteristics on each side of the contact zone complicating the process ofmixing different numerical techniques. In this work a displacement contact frame is inserted betweenthe FE and BE interface meshes, discretized and finally connected to the contacting substructuresusing LLMs collocated at the mesh-interface nodes. This methodology will provide a partitionedformulation which preserves software modularity and facilitates the connection of non-matching FEand BE meshes.

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

High-speed metal cutting processes can cause extremely rapid heating of the work material. Temperature on the machined surface is critical for surface integrity and the performance of a precision component. However, the temperature of a machined surface is challenging for in-situ measurement.So, the finite element(FE) method used to analyze the unique nonlinear problems during cutting process. In terms of heat-force coupled problem, the thermo-plastic FE model was proposed to predict the cutting temperature distribution using separated iterative method. Several key techniques such as material constitutive relations, tool-chip interface friction and separation and damage fracture criterion were modeled. Based on the updated Lagrange and arbitrary Lagrangian-Eulerian (ALE) method, the temperature field in high speed orthogonal cutting of carbon steel AISI-1045 were simulated. The simulated results showed good agreement with the experimental results, which validated the precision of the process simulation method. Meanwhile, the influence of the process variables such as cutting speed, cutting depth, etc. on the temperature distribution was investigated.

Abstract Within complex structures it is not uncommon for localised nonlinearities to be present, this renders conventional linear mid-high frequency analysis techniques such as the Hybrid Finite Element (FE) - Statistical Energy Analysis (SEA) method inapplicable. The development of a linearisation procedure applicable to an ensemble of random systems featuring deterministic nonlinearity is initially considered in this work, which is centred around the technique of Equivalent Linearisation. Constraining the linearisation to remain invariant across the whole ensemble, key to the linearised hybrid formulation developed, produced a relation between the order of both nonlinearity and the required statistical response moment when considered for Gaussian excitation. From the linearisation derived, an extension to hybrid variance theory was necessary to determine the variance of a frequency integrated response of the master system. A numerical study is then used to demonstrate the linearised Hybrid FE-SEA method against a series of Monte Carlo benchmark simulations adopting a Lagrange Rayleigh-Ritz model. The benchmark simulations feature different treatments of the nonlinearity from the linearisation developed to the full nonlinear solution.

In this paper, Elliptic control problems with pointwise box constraints on the state is considered, where the corresponding Lagrange multipliers in general only represent regular Borel measure functions. To tackle this difficulty, the Lavrentiev regularization is employed to deal with the state constraints. To numerically discretize the resulted problem, full piecewise linear finite element discretization is employed. Estimation of the error produced by regularization and discretization is done. The error order of full discretization is not inferior to that of variational discretization because of the Lavrentiev-regularization. Taking the discretization error into account, algorithms of high precision do not make much sense. Utilizing efficient first-order algorithms to solve discretized problems to moderate accuracy is sufficient. Then a heterogeneous alternating direction method of multipliers (hADMM) is proposed. Different from the classical ADMM, our hADMM adopts two different weighted norms in two subproblems respectively. Additionally, to get more accurate solution, a two-phase strategy is presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the hADMM. Numerical results not only verify error estimates but also show the efficiency of the hADMM and the two-phase strategy.

Aims. We investigate the metallicity, age, and orbital anatomy of the inner Milky Way, specifically focussing on the outer bar region. Methods. We integrated a sample of APOGEE DR16 inner Galaxy stars in a state of the art bar-bulge potential with a slow pattern speed and investigated the link between the resulting orbits and their [Fe/H] and ages. By superimposing the orbits, we built density, [Fe/H], and age maps of the inner Milky Way, which we divided further using the orbital parameters eccentricity, |Xmax|, and |Zmax|. Results. We find that at low heights from the Galactic plane, the Galactic bar gradually transitions into a radially thick, vertically thin, elongated inner ring with average solar [Fe/H]. This inner ring is mainly composed of stars with AstroNN ages between 4 and 9 Gyr with a peak in age between 6 and 8 Gyr, making the average age of the ring ∼6 Gyr. The vertical thickness of the ring decreases markedly towards younger ages. We also find very large L4 Lagrange orbits that have average solar to super-solar metallicities and intermediate ages. Lastly, we confirm a clear X-shape in the [Fe/H] and density distributions at large Galactic heights. Conclusions. The orbital structure obtained for the APOGEE stars reveals that the Milky Way hosts an inner ring-like structure between the planar bar and corotation. This structure is on average metal rich, intermediately aged, and enhances the horizontal metallicity gradient along the bar’s major axis.

A novel contact model is presented to efficiently solve a face-mask contact problem by using the finite element (FE) method for the optimized design of a custom facial mask. Simulation of contact pressure for various mask designs considering material properties of the face allows virtual evaluation of the suitability of a mask design for a person’s face without conducting empirical measurement of the face-mask contact pressure. The proposed contact model is accomplished by combining three approaches to reduce the calculation cost of simulating the face-mask contact: (1) use of a simplified and modifiable mask model that applies a spline curve to design points; (2) reduction of the FE model of the face by applying static condensation; and (3) application of a contact assumption that uses the Lagrange multiplier method. A numerical case study of a medical mask design showed that the proposed model could calculate the face-mask contact pressure efficiently (0.0448 sec per design). In a pilot usability experiment, the measured contact pressure was found similar values (range of mean contact pressure: 0.0093 ~ 0.0150 MPa) to the estimated values (range of mean contact pressure: 0.0097 ~ 0.0116 MPa).

To better understand the corrosion and corrosion products behavior in the primary circuit of lead-bismuth eutectic (LBE) coolant reactor, the concentration distribution of soluble impurities and the transport of solid particles are investigated through the finite-element method. An axisymmetric model of the primary circuit of an LBE reactor was constructed to accelerate the calculation of the thermal hydraulic filed of the circuit. The saturation concentration of solute Fe, Cr and Ni in LBE coolant are identified through the equilibrium of their oxides and PbO, and the very different saturation concentrations of Fe/Cr/Ni in LBE will lead to significant element-selective corrosion. The migration of solid oxide particles in the primary circuit is also investigated by the Euler–Lagrange tracing model. The simulation shows that driving force for the movement of particles >100 μm is buoyancy, which lets particles float on a free surface, while particles <10 μm tend to suspend in coolant. However, the behavior of particles also depends on the formation position, the particles formed above the core have a high possibility of re-entering in the core.

The magnetic pressure seam welding is one of the candidate methods to join thin sheet smart and multifunctional materials. In this research, to examine the mechanism of magnetic pressure welding from a dynamic viewpoint, numerical simulation of the impact was carried out by using a commercial Euler-Lagrange coupling software MSC.Dytran (MSC.Software) as a first step of the computational studies, where the joint between Fe and Al was employed according to the previous experimental researches. From the serial numerical results, it was found that the increase of temperature at the joint interface was not enough to melt Al or Fe in the range of collision velocity and angle studied in this report. Also, it was revealed that the very large mean stress occurred at the interface which could be considered as the pressure at joint interface and Al moved with high velocity along the interface. Moreover, it was found that there were two patterns of plastic strain distribution near the joint interface depending on the collision velocity and collision angle. Finally, it can be concluded that the plastic strain pattern might be related to the success of magnetic pressure seam welding.

The present paper proposes a linearised hybrid finite element-statistical energy analysis (FE-SEA) formulation for built-up systems with nonlinear joints and excited by random, as well as harmonic, loadings. The new formulation was validated via an ad-hoc developed stochastic benchmark model. The latter was derived through the combination of the Lagrange-Rayleigh-Ritz method (LRRM) and the Monte Carlo simulation (MCS). Within the build-up plate systems, each plate component was modelled by using the classical Kirchhoff’s thin-plate theory. The linearisation processes were carried out according to the loading-type. In the case of random loading, the statistical linearisation (SL) was employed, while, in the case of harmonic loading, the method of harmonic balance (MHB) was used. To demonstrate the effectiveness of the proposed hybrid FE-SEA formulation, three different case studies, made-up of built-up systems with localized cubic nonlinearities, were considered. Both translational and torsional springs, as joint components, were employed. Four different types of loadings were taken into account: harmonic/random point and distributed loadings. The response of the dynamic systems was investigated in terms of ensemble average of the time-averaged energy.

Background: In this paper, four-years (21st October, 2018 – 21st October, 2022) cryptocurrencies indicators such as OPP, CPP, HGP, LOP, and ATV for six (6) crypto assets with high market capitalization based on coin categorization/utilization were considered as explanatory (independent) variables to estimate crypto assets returns. Aim: This study seek to evaluate the relationship between crypto asset indicators and crypto market capitalization, so as to quantitatively review and establish that crypto market capitalization can easily be influenced by crypto indicators. Method: The study uses three-panel data models, the pooled OLS, fixed effect (FE) and random effect (RE) changes, to evaluate crypto assets returns for the cross-sectional data of these six crypto assets. Results: The study revealed that all three-panel models fit the data; the result also shows that FE and RE models explain about 62% and 50%, respectively of the return variance on the total market capitalization (MCap). While, Pooled OLS model could only explain 42% variation on the total market capitalization (MCap). The Hausman test result indicates that the FE model is an appropriate model to estimate the cross-sectional variables when compared to the RE model. Also, the Lagrange Multiplier (LM) test statistic with corresponding p-value for FE and RE when compared to the pooled OLS are 32.117 (0.0000*) and 38.943 (0.0000*), respectively, indicating that both the FE and RE models are more appropriate than the Pooled OLS model when compared with each. The identified crypto indices employed are significant and positively affects the market capitalization of these crypto assets. Finally, the study reveals that crypto assets can be classified and considered as economic assets since they include monetary values and investors derive economic benefits in terms of holding gain/losses and other benefits

Cams are considered as one of the most important mechanical components that depends the contact action to do its job and suffer a lot of with drawbacks to be predicted and overcame in the design process. this work aims to investigate the induced cam contact and the maximum shear stress energy or (von misses) stresses during the course of action analytically using Hertz contact stress equation and the principal stress formulations to find the maximum stress value and its position beneath the contacting surfaces. The experimental investigation adopted two dimensions photoelastic technique to analyze cam stresses under a plane polarized light. The problem has been numerically simulated using Ansys software version 15 as FE solver and depending on Lagrange and Penalty contact algorithm. The effect of cam geometry, characterized by some parameters such as follower radius, face width, rise and return angles, and modulus of elasticity on the contact stress is investigated aiming to minimize the induced stresses.

Introduction. When numerically solving problems of elasticity theory in a three-dimensional formulation by the finite element method, finite elements (FE) in the form of parallelepipeds, prisms and tetrahedra are used. Regularly, the construction of stiffness matrices of volumetric FE is based on the principle of isoparametricity, which involves the Lagrange polynomials to approximate the geometry and displacements. In computational practice, the most widespread FE are the so-called multilinear isoparametric FE with a linear law of approximation of displacements. The main disadvantage of these elements lies in the “locking” effect when modulating bending deformations. Moreover, the error of the numerical solution increases drastically in the case when the structure, in comparison to conventional deformations, undergoes significant displacements as a rigid whole. Long-term experience in solving problems of deformable solid mechanics by the finite element method has shown that existing volumetric FE have slow convergence, specifically, when modeling bending deformations of plates and shells. This study aims at constructing stiffness matrices of multilinear volumetric FE of increased accuracy allowing for rigid displacements based on the double approximation method.Materials and Methods. The mathematical apparatus of the double approximation method based on the principle of a separate representation of the distribution functions of displacements and deformations inside the element, was used to construct the stiffness matrices of volumetric FE. The storage and processing of the resulting system of equations was implemented in algorithmic terms of sparse matrices. Software development and computational experiments were carried out using the Microsoft Visual Studio 2013 64-bit computing platform and the Intel ® Parallel Studio XE 2019 compiler with the integrated Intel ® Visual Fortran Composer XE 2019 text editor. Visualization of the calculation results was performed using the descriptor graphics of the MATLAB computer mathematics package. A large eight-node SOLID185 CE of the ANSYS Mechanical software complex was used as a test sample.Results. Mathematical tool and software were developed to study the stress-strain state of massive structures under various types of external actions. The authorized application software package was verified on test examples with known analytical solutions. It has been shown that the constructed FE accurately satisfy the basic requirements for finite element modeling of spatial problems of elasticity theory.Discussion and Conclusion. The performed testing of the developed mathematical and program toolkit has shown that the finite elements constructed on the basis of the double approximation method can successfully compete with similar SOLID185 volumetric elements of the ANSYS Mechanical software complex. The proposed elements can be integrated into domestic import-substituting software systems that implement the finite element method in the form of the displacement method.

Explosively formed projectiles (EFPs) are widely used in civil applications and the military field for their excellent impact performance. How to give full play to the energy accumulation effect of explosives and improve the penetration performance has become the main problem of EFP design. The aim of the present study was to investigate the effect of liner structure on EFP formation and its penetration behavior. In order to achieve this, a finite element (FE) model was first established on the basis of the Lagrange and ALE method. Then, formation and penetration performance tests of EFP were performed to verify the validity and feasibility of the proposed FE model, where the configuration, velocity of EFP, and penetration diameter left on the target plate were compared. Finally, by using the proposed FE model, the entire process of the formation and penetration behavior of EFP with axial symmetrical variable thickness liners were analyzed, where spherical-segment liners with uniform and non-uniform thickness were developed. The results were drawn as follows: the numerical simulation error of EFP velocity was less than 5%, and the simulated penetration diameter was compared to the 8.6% error obtained from the experimental method. It demonstrated that the proposed FE model had higher prediction precision. After the explosive was detonated, a forward-folding EFP was formed by the liner with a thin edge thickness, while the EFP formed by the liner with uniform thickness had a backward-folded configuration. It was also found that the liner with a thin edge thickness gave the largest steady velocity of EFP, and it was the lowest by using the liner with uniform thickness. There were two types of loads generated after the formation of an EFP, those were shock wave loading and an EFP, both causing damage in the target plate during the process of an EFP’s penetration into it. The shock wave induced by liners with non-uniform thickness caused higher damage in the target plate, the maximum value of stress was reached at about 4.0 GPa. The forward-folding EFP formed by the liner with the thinnest edge thickness had the largest penetration ability. The backward-folded EFP, owing to the hollow structure, had the worst penetration ability, which failed to penetrate the target plate.

There are several techniques to simulate rebar reinforced concrete, such as smeared model, discrete model, embedded model, CLIS (constrained Lagrange in solid) model, and CBIS (constrained beam in solid) model. In this study, however, the interaction between the concrete elements and the reinforcement beam elements is only simulated by the discrete model and CBIS (constrained beam in solid) model. The efficiency and accuracy comparisons are investigated with reference to the analysis results by both models provided by LS-DYNA explicit finite element software. The geometric models are created using LS-PrePost, general purpose preprocessing software for meshing. The meshed models are imported to LS-DYNA where the input files are then analyzed. Winfrith and CSCM concrete material options are employed to describe the concrete damage behavior. The reinforcement material model is capable of isotropic and kinematic hardening plasticity. The load versus midspan deflection curves of the finite element models correlate with those of the experiment. Under the conditions of the same level of accuracy, the CBIS model is evaluated to have the following advantages over the discrete model. First, it has the advantage of reducing the time required for FE modeling; second, saving computer CPU time due to a reduction in total number of nodes; and third, securing a good aspect ratio of concrete elements.

This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is the modelling of the reinforcing fibers of the orthotropic layers assuming a non-uniform distribution in the thickness direction. The Halpin–Tsai approach is employed to define the overall mechanical properties of the composite layers starting from the features of the two constituents (fiber and epoxy resin). Several functions are introduced to describe the dependency on the thickness coordinate of their volume fraction. The analyses are carried out in the theoretical framework provided by the first-order shear deformation theory (FSDT) for laminated thick plates. Nevertheless, the same approach is used to deal with the vibration analysis of thin plates, neglecting the shear stiffness of the structure. This objective is achieved by properly choosing the value of the shear correction factor, without any modification in the formulation. The results prove that the dynamic response of thin and thick plates, in terms of natural frequencies and mode shapes, is affected by the non-uniform placement of the fibers along the thickness direction.

This paper presents a modified variational method for free and forced vibration analysis of coupled beam systems resting on various viscoelastic foundations. Non-uniform as well as uniform curved and straight Timoshenko beam components are considered in the coupled beam system. Using proper coordinate transformations, interactions among the beam components of the coupled beam system are accommodated by combining Lagrange multiplier method and least-square weighted residual method. Interface potential energy for various boundary conditions including the elastic ones is simultaneously formulated. Thus, the proposed method allows flexible choice of the admissible functions, regardless of the boundary conditions. Based on the proposed energy method, Winkler, Pasternak or even variable foundations distributed in a parabolic or sinusoidal manner can be easily introduced into the coupled beam systems. Two kinds of damping, namely the proportional and viscous damping, are also employed to model the energy dissipation of the viscoelastic foundations. Corresponding finite element (FE) simulations are performed where possible and good agreement is observed. Thus, great efficiency and accuracy of the present approach are demonstrated for free, steady-state and transient vibration of the coupled beam systems. The influences of the parameters of the variable viscoelastic foundations on the dynamic properties of the coupled beam system are also examined.

Dynamic substructuring is now a well established and powerful tool for engineers used to analyze the dynamic response of mechanical systems. The technique is particularly favored for the simulation of mechanical vibrations allowing different aspects to be studied. It consists in splitting the global structure into several substructures from which reduced models are built. In Finite Element software, these reduced models, also called superelements, are generally built using the concept of Component Mode Synthesis. Difficulties arise when structures made of frequency-dependent materials are considered since classical modal reduction algorithms are inapplicable as they are because of the frequency-dependence of the stiffness matrix. Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. The methodology takes advantage of the Golla-Hughes-McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The coupling of the superelement with a host structure is achieved via the use of Lagrange multipliers. The reduced system takes the form of a constant matrix of very small size compared to the original FE model. The method is applied to laminated panels such as an automobile windscreen.

Object and purpose of research. The study focuses on management of dynamic parameters of structures, the load on which has unsteady character in accordance with a given frequency spectrum. Based on the earlier obtained [8, 15] matrix relations of sensitivity analysis, effective design iteration algorithms, which satisfy Kuhn–Tucker optimum conditions, are developed and implemented in software. Materials and methods. The methods used are a displacement method version of the beam finite-element technique, analytical and semi-analytical methods of taking a derivative with respect to frequencies, shapes as well as unsteady displacements of structure integrally averaged in space and time, methods of simple iterations with relaxation smoothening, methods of linearization of recurrent relations of optimality conditions and reduction of conditional minimization problem to unconditional problem using Lagrange factors. Main results. For FE beam model with a large number of finite elements, minimization mass problems are solved at restricted integral norm of deflection for various unsteady excitation at a given time interval. Comparison of optimization procedures are made for accuracy and efficiency using direct implicit differentiation of difference scheme and normal mode method for response. Conclusion. Similar results are obtained by different methods of calculating the unsteady response and performance of sensitivity analysis. Efficient management of the mass and stiffness distribution is demonstrated with a relatively high gain in isoperimetric formulation.

To decrease the opening shock as well as improve the resistance coefficient and stability of the parachute of aviation weapon under subsonic conditions, a new kind of high-damping four-winged rotating (HFWR) parachute is investigated in this paper. The transient dynamic behavior and aerodynamic characteristics of the parachute during the inflation process are studied. Considering the permeability, the 3D folded finite element (FE) model of the HFWR parachute is established based on the direct folding modeling technique, and the inflation process of the parachute under subsonic flow is simulated using the multimaterial arbitrary Lagrange–Euler (ALE) method. A series of wind tunnel tests are conducted to verify the numerical results. Besides, the opening performances of the HFWR parachute and the round parachute, which includes the inflation process, the dynamic response of the swing angle, and the opening shock load varying with time, are compared under the same conditions. The results show that the opening performance of the HFWR parachute is superior to the round parachute under specific military background. The fluid-structure interaction (FSI) simulation results show good consistency with the wind tunnel tests, which indicates that the numerical modeling can effectively simulate and predict the opening performance and aerodynamic characteristics of the rotating parachute. The modeling method in this paper can help shorten the development cycle, improve the cost effectiveness, and optimize the design of the parachute.

Among all the common mechanical transmission elements, gears still playing the most dominant role especially in the heavy duty works offering extraordinary performance under extreme conditions and that the cause behind the extensive researches concentrating on the enhancement of its durability to do its job as well as possible. Contact stress distribution within the teeth domain is considered as one of the most effective parameters characterizing gear life, performance, efficiency, and application so that it has been well sought for formal gear profiles and paid a lot of attention for moderate tooth shapes. The aim of this work is to investigate the effect of pressure angle, speed ratio, and correction factor on the maximum contact and bending stress value and principal stresses distribution for symmetric and asymmetric spur gear. The analytical investigation adopted Hertz equations to find the contact stress value, distribution, and the contact zone width while the numerical part depends on Ansys software version 15, as a FE solver with Lagrange and penalty contact algorithm. The most fruitful points to be noticed are that the increasing of pressure angle and speed ratio trends to minimize all the induced stresses for the classical gears and the altered teeth shape with larger loaded side pressure angle than the unloaded side one behave better than the symmetric teeth concerning the stress reduction.

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.

Terdapat fenomena penelitian ini yaitu : Diluncurkan bank pakan untuk meningkatkan kualitas dan produksi ternak, Impor gandum menjadi opsi alternatif yang diberikan pemerintah untuk menghadapi risiko kenaikan harga pakan, Memastikan dua perusahaan (PT Japfa Comfeed dan PT Charoen Pokphand (CP) Indonesia) menyerap jagung dari petani dan stoknya tercukupi saat panen raya, diharapkan harga jagung tidak anjlok dan berada pada titik keseimbangannya seperti biasanya, dan Pakan ternak diprediksi mengalami kenaikan pada periode kuartal akhir dan menariknya saham JPFA dan MAIN. Dari fenomena diatas, maka peneliti tertarik untuk mendalami aset lancar, total aset, utang lancar, persediaan dari perusahaan pakan ternak yang terdaftar di Bursa Efek Indonesia. Rumusan masalah observasi ini ialah bagaimana pengaruh Current Aset, Quick Aset, terhadap ukuran perusahaan studi empiris pada perusahaan sector industri dasar kimia sub sector pakan ternak yang terdaftar di Bursa Efek Indonesia secara parsial maupun simultan. Observasi ini bertujuan untuk mengetahui, mengetest juga menganalisa pengaruh current aset, quick aset dan ukuran perusahaan apakah saling berpengaruh, atau sejalan dengan fenomena tersebut secara parsial ataupun simultan. Jenis penelitian ini ialah kuantitatif. Dalam observasi ini menghasilkan sampel uji sebanyak 5 perusahaan pakan ternak, peneliti melanggunakan data selama 3tahun dari tahun 2019-2021 sehingga menghasilkan data observasi selama periode penelitian 2019-2021 sebanyak 45 data. Dan diolah menggunakan aplikasi Eviews 12, dalam aplikasi eviews terdapat tiga (3) metode yaitu Common Effect (CE), Fixed Effect (FE), dan Random Effect (RE). Aplikasi Eviews melakukan beberapa test seperti: Chow Test, Hausman Test, Lagrange Multiplier Test, Uji Multikolinearitas, Uji Autokolerasi, Uji Heteroskedastisitas, Uji Normalitas, Panel Least Squares. Variabel Quick Ratio dalam model penelitian ini secara parsial memiliki berpengaruh terhadap variabel ukuran perusahaan dengan nilai Probabilitas 0.02 (< 0.05) sedangkan variabel Current Ratio dalam model penelitian ini secara parsial tidak memiliki pengaruh terhadap variabel ukuran perusahaan dengan nilai Probabilitas 0.10 (> 0.05). Variabel Quick Ratio, Current Ratio secara simultan memiliki pengaruh terhadap ukuran perusahaan dengan nilai Prob(F-statistic) < 0,05 sebesar 0.00. Kelayakan variabel Quick Ratio, Current Ratio terhadap ukuran perusahaan sebesar 31,73%, sedangkan sisanya dipengaruhi oleh variabel lain, berupa utang jangka panjang, asset tetap, modal, penjualan, bunga, pajak, harga saham, dsb.

Abstract In this work, a two-dimensional finite element (FE) model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model). It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.

AbstractWe present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange’s principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values.

The dynamic characteristics, in the uprising phase, of an overhead crane carrying two carriages and a cylindrical payload are studied in this article. The crane system investigated mainly consists of a twin beam, two carriages, a rigid payload, and two wire ropes. A new analytical model, in which the beam, carriages, payload, and wire ropes are, respectively, considered as uniform Euler—Bernoulli beam, lumped masses, rigid body, and springs, is presented to describe the uprising dynamics of the specific crane system. The most distinguished characteristic of the model is the dynamic coupling deriving from the presence of a flexible beam, carriages, and the cylindrical payload. The kinetic and potential energies, during the pre-tensing and lifting phases, of the components in the system are presented in particular. Then, utilizing the Rayleigh—Ritz method, one can obtain the differential equations of the dynamic system substituting the energy into Lagrange's equation. The differential equations are numerically solved by the fourth-order Runge—Kutta method, and then some useful results representing the dynamic features of the system are obtained according to the calculation. The validity of the analytical model is demonstrated by an equivalent FE model created by ANSYS and ADAMS. Comparison of the results, obtained by two distinct approaches, indicates good agreements, which can be the validity evidence of the analytical model.

RESUMENEl objetivo de este artículo es reflexionar sobre los mecanismos de financiación y de control de las instituciones religiosas por los laicos en las primeras décadas de la conquista y colonización de Hispanoamérica. Investigar sobre la inversión laica en lo sagrado supone en un primer lugar aclarar la historiografía sobre laicos, religión y dinero en las sociedades de Antiguo Régimen y su trasposición en América, planteando una mirada desde el punto de vista de las motivaciones múltiples de los actores seglares. A través del ejemplo de restituciones, donaciones y legados en losAndes, se explora el papel de los laicos españoles, y también de las poblaciones indígenas, en el establecimiento de la densa red de instituciones católicas que se construye entonces. La propuesta postula el protagonismo de actores laicos en la construcción de un espacio cristiano en los Andes peruanos en el siglo XVI y principios del XVII, donde la inversión económica permite contribuir a la transición de una sociedad de guerra y conquista a una sociedad corporativa pacificada.PALABRAS CLAVE: Hispanoamérica-Andes, religión, economía, encomienda, siglos XVI y XVII.ABSTRACTThis article aims to reflect on the mechanisms of financing and control of religious institutions by the laity in the first decades of the conquest and colonization of Spanish America. Investigating lay investment in the sacred sphere means first of all to clarifying historiography on laity, religion and money within Ancien Régime societies and their transposition to America, taking into account the multiple motivations of secular actors. The example of restitutions, donations and legacies inthe Andes enables us to explore the role of the Spanish laity and indigenous populations in the establishment of the dense network of Catholic institutions that was established during this period. The proposal postulates the role of lay actors in the construction of a Christian space in the Peruvian Andes in the sixteenth and early seventeenth centuries, when economic investment contributed to the transition from a society of war and conquest to a pacified, corporate society.KEY WORDS: Hispanic America-Andes, religion, economics, encomienda, 16th and 17th centuries. BIBLIOGRAFIAAbercrombie, T., “Tributes to Bad Conscience: Charity, Restitution, and Inheritance in Cacique and Encomendero Testaments of 16th-Century Charcas”, en Kellogg, S. y Restall, M. 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IntroductionThe relationship between the twisting of the three subtendons of the Achilles tendon (AT) and local strain has received attention in recent years. The present study aimed to elucidate how the degree of twist in the AT affects strain using finite element (FE) analysis, while also considering other geometries (e.g., length, thickness, and width) and their combinations.MethodsA total of 59 FE models with different degrees of twist and geometries were created. A lengthening force (z-axis) of 1,000 N was applied to each subtendon (total: 3,000 N). The average value of the first principal Lagrange strain was calculated for the middle third of the total length of the model.ResultsStatistical (stepwise) analysis revealed the effects of the degree of twist, other geometries, and their combinations on AT strain. The main findings were as follows: (1) a greater degree of twist resulted in higher average strains (t = 9.28, p &lt; 0.0001) and (2) the effect of the degree of twist on the strain depended on dimensions of thickness of the most distal part of the AT (t = −4.49, p &lt; 0.0001) and the length of the AT (t = −3.82, p = 0.0005). Specifically, when the thickness of the most distal part and length were large, the degree of twist had a small effect on the first principal Lagrange strain; however, when the thickness of the most distal part and length were small, a greater degree of twist results in higher first principal Lagrange strain.ConclusionThese results indicate that the relationship between the degree of twist and local strain is complex and may not be accurately assessed by FE simulation using a single geometry.

Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally challenging. We employ an unfitted Finite Element (FE) framework for the discretization of the domains and develop a tailored, globally convergent, and efficient multigrid method for solving contact problems on the internal interfaces. In the unfitted FE methods, structured background meshes are used and only the underlying finite element spaces are modified to incorporate the discontinuities. The non-penetration conditions on the embedded interfaces of the domains are discretized using the method of Lagrange multipliers. We reformulate the arising variational inequality problem as a quadratic minimization problem with linear inequality constraints. Our multigrid method can solve such problems by employing a tailored multilevel hierarchy of the FE spaces and a novel approach for tackling the discretized non-penetration conditions. We employ pseudo-L2 projection- based transfer operators to construct a hierarchy of nested FE spaces from the hierarchy of non-nested meshes. The essential component of our multigrid method is a technique that decouples the linear constraints using an orthogonal transformation. The decoupled constraints are handled by a modified variant of the projected Gauss–Seidel method, which we employ as a smoother in the multigrid method. These components of the multigrid method allow us to enforce linear constraints locally and ensure the global convergence. We will demonstrate the robustness, efficiency, and level independent convergence property of the proposed method for Signorini’s problem and two-body contact problems

Purpose The purpose of this paper is to present an applied method to design the low-speed contact between a mass and surface of a beam using an analytical solution based on the first-order shear deformation beam theory. Also, a simulation of impact process is carried out by ABAQUS finite element (FE) code. Design/methodology/approach In theoretical formulation, first strains and stresses are obtained, then kinetic and potential energies are written, and using a combination of Ritz and Lagrange methods, a set of system of motion equations in the form of mass, stiffness and force matrices is obtained. Finally, the motion equations are solved using Runge–Kutta fourth order method. Findings The von Mises stress contours at the impact point and contact force from the ABAQUS simulation are illustrated and it is revealed that the theoretical solution is in good agreement with the FE code. The effect of changes in projectile speed, projectile diameter and projectile mass on the results is carefully examined with particular attention to evaluate histories of the impact force and beam recess. One of the important results is that changes in projectile speed have a greater effect on the results than changes in projectile diameter, and also changes in projectile mass have the least effect. Originality/value This paper presents a combination of methods of energy, Ritz and Lagrange and also FE code to simulate the problem of sandwich beams under low velocity impact.

A comprehensive numerical model is developed using Lagrangian finite element (FE) formulation for investigating the steady-state viscoelastic (VE) rolling contact response. Schapery's nonlinear viscoelastic (NVE) model is adopted to simulate the VE behavior. The model accounts for large displacements and rotations. A spatially dependent incremental form of the VE constitutive equations is derived. The dependence on the history of the strain rate is expressed in terms of the spatial variation of the strain. The Lagrange multiplier approach is employed. The classical Coulomb's friction law is used. The developed model is verified and its applicability is demonstrated.

The aim of this technical brief is to provide a new viewpoint of friction factor for contact stress calculations of gears. The idea of friction factor has been coined, for the calculation of contact stresses along the tooth contact for different helical gear pairs. Friction factors were developed by evaluating contact stresses with and without friction for different gear pairs. In this paper, three-dimensional (3D) finite element method (FEM) and Lagrange multiplier algorithm have been used to evaluate the contact stresses. Initially, a spur gear finite element (FE) model was validated with the theoretical analysis under frictionless condition, which is based on Hertz's contact theory. Then, similar FE models were constructed for 5 deg, 15 deg, 25 deg, and 35 deg helical gear pairs. The contact stresses of these models were evaluated for different coefficients of friction. These results were employed for the development of friction factor.

Several present-day applications require the joining of dissimilar materials by solid-state processes. Aluminum-stainless steel sheet metal joining finds its application in the Automotive industry. In present work, two dissimilar sheet metal workpieces of Aluminium and Stainless Steel were joined with a newly developed Friction Crush Welding (FCW) process. Macro-structure images along with an X-ray diffraction (XRD) pattern were used to investigate the prepared samples, and a hook-like structure was found along with a U-shaped interface and intermetallic phases such as FeAl2, Fe2Al5, FeAl3, Al, and ϒ-Fe. The work aims to develop a novel Finite Element (FE) model based on ABAQUS for FCW of Aluminium-Stainless Steel. The FE model was developed as a three-dimensional, explicit nonlinear model utilizing the Lagrange technique. The developed FE model was validated by comparing the FE model results with experimental temperature data obtained by infrared thermography. The predicted temperature values from the FE model are in excellent agreement with the experimentally measured values. The influence of welding variables, i.e., tool rotational speed (2000, 3000, and 4000 rpm) and welding speed (15, 30, and 45 mm/min), on temperature, was also investigated. It was found that increasing tool rotational speed increases temperature but decreases stress distribution, whereas the correlation between feed rate and temperature was inversely proportional. Results show that the best weld structure was obtained when welding was performed at a welding speed of 30 mm/min and tool rotational speed of 3000 rpm. The developed FE model may be used to predict the temperature and weld structure.

In the process of aircraft structural design, the aerodynamic load and inertial load need to be distributed from single loading points to distributed finite element (FE) nodes before strength analysis. The most commonly used loading distribution method is a Multi-Point Arrangement (MPA) method, which introduces a one-dimensional Lagrange multiplier based on the principle of minimum deformation energy, and simplifies the special-shaped 3D surface in aircraft structure to a plane. However, the actual aircraft structure contains a large number of special-shaped surfaces, and the MPA method cannot accurately distribute the loads on these complex special-shaped surfaces, affecting the accuracy of strength analysis. This paper developed a new 3D load distribution method based on multi-dimensional Lagrange multipliers (MDLM), which can simultaneously achieve an efficient and accurate distribution of surface aerodynamic loads and inertial loads in all directions. Typical numerical cases showed that when an aircraft structure model is a plane, this MDLM method converges to the traditional MPA method. For 3D special-shaped surfaces, the average error of this MDLM method is 0.77–2.28%, which is significantly smaller than the average error of the traditional MPA method (3.30–7.40%).

PurposeThis article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.Design/methodology/approachFirst, the system of linear equations corresponding to the linear constraints is solved for the leading variables in terms of the free variables and the constants. Then, the reduced system of equilibrium equations with respect to the free variables is derived from the finite-dimensional virtual work equation. Finally, the algorithm is designed.FindingsThe proposed procedure is promising in three typical cases: (1) to enforce displacement constraints in any direction; (2) to implement local refinements by allowing hanging nodes from element subdivision and (3) to treat non-matching grids of distinct parts of the problem domain. The procedure is general and suitable for 3D non-linear analyses.Research limitations/implicationsThe algorithm is fitted only to the Galerkin-based numerical methods.Originality/valueThe proposed procedure does not need Lagrange multipliers or penalties. The tangential stiffness matrix of the reduced system of equilibrium equations reserves positive definiteness and symmetry. Besides, many contemporary Galerkin-based numerical methods need to tackle the enforcement of the essential conditions, whose weak forms reduce to linear constraints. As a result, the proposed procedure is quite promising.

AbstractThe analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results.

The nonlinear finite element (FE) modeling approach has been adopted to model and predict the modal responses of the combined damaged (crack and delamination) layered shell structures. The damaged panel structure has been constructed mathematically using a circular meshing approach of the FE technique to include the crack. Similarly, the sublaminate approach has being used to introduce delamination of the layered structure on a mutual center. The structural distorted geometry and the deformations were modeled through the full geometrical nonlinear strain-displacement (Green–Lagrange) relations in association with higher-order polynomial functions. The modal responses of the damaged structure were obtained through an iterative method in association with the nonlinear FE technique. The predicted response accuracies were established with two-step verifications: that is, the numerical solution stability (elemental sensitivity) and the degree of deviation with published data. The maximum deviation between the developed numerical model and the reference result (first-order shear deformation theory) was 8.3%. The model’s competence and responses were compared with experimental data, with and without damages. Finally, new examples have been solved for different structural geometry-dependent parameters (shell configurations, delamination shapes, crack positions/lengths, end boundaries, etcetera) affecting final modal values. A detailed in-depth understanding of the damage and curvature (unequal/equal curvature) effects on modal responses will be discussed.

In this article, the nonlinear bending behavior of functionally graded (FG) curved (cylindrical, hyperbolic, and elliptical) panel is investigated under combined thermomechanical loading. In this study, two temperature fields (uniform and linear) across the thickness of shell panel are considered. The panel model is developed mathematically using higher-order shear deformation midplane kinematics with Green–Lagrange-type nonlinear strains. The individual constituents of functionally graded material (FGM) are assumed to be temperature-dependent (TD) and graded continuously using the power-law distribution. The effective material properties of FG shell panel are evaluated based on Voigt's micromechanical model. The governing equation of the panel structure is obtained using the variational principle and discretized through suitable finite-element (FE) steps. A direct iterative method is employed to compute the desired responses of the curved panel structure. The efficacy of the present nonlinear model has been shown by comparing the responses with those available published literature and commercial FE tool ansys. Finally, the model has been extended to examine the effect of various parameters (volume fractions, temperature, thickness ratios, curvature ratios, aspect ratios, and support conditions) on the nonlinear bending behavior of curved FG panel by solving wide variety of numerical illustrations.

We proposed herein a unique method of insulator-decorated bipolar electrochemistry (IDBE), for realizing large-scale separation of bioparticles in microchannels driven by AC dielectrophoresis (DEP). In IDBE, a pair of planar driving electrodes (DE) is placed at the bottom of channel sidewalls, between which an array of the rectangular floating electrode (FE) strips without external Ohmic contact are evenly spaced along transversal direction, and a series of insulating dielectric blocks are periodically deposited above all the inter-electrode gaps and in full contact with the channel bottom surface. By creating local field maximum and minimum at multiple sites, IDBE extends well the actuating range of DEP force field from the immediate vicinity of electrode tips in traditional bipolar electrochemistry to current fluid bulk. Considering DEP force plays the dominant role around 1MHz, we utilize Lagrange particle tracing algorithm to calculate motion trajectories of incoming samples for testing the feasibility of microchip in continuous separation of live and dead yeast cells. By applying suitable voltage parameters, highly efficient DEP sorting is theoretically achievable under a moderate inlet flow rate, where most of the viable yeasts are trapped by positive-DEP to sharp dielectric edges, while all the incoming nonviable yeasts are repelled by negative-DEP to the top surface of both FE and insulating block to form multiple thin beams co-flowing into the channel outlet. The microfluidic device exploiting insulators on bipolar FE effectively expands the actuating range of nonlinear electrodynamics and provides invaluable guidelines for developing flexible electrokinetic frameworks in modern microfluidic systems.

AbstractClimate change necessitates exploring innovative geoengineering solutions to mitigate its effects—one such solution is deploying planetary sunshade satellites at Sun–Earth Lagrange point 1 to regulate solar radiation on Earth directly. However, such long-span space structures present unique technical challenges, particularly structural scalability, on-orbit manufacturing, and in-situ resource utilization. This paper proposes a structural concept for the sunshade’s foil support system and derives from that a component-level modular system for long-span fiber composite lightweight trusses using coreless filament winding. Within a laboratory-scale case study, the component scalability, as well as the manufacturing and material impacts, were experimentally investigated by bending deflection testing. Based on these experimental results, FE models of the proposed structural concept were calibrated to estimate the maximum displacement and mass of the foil support structure, while comparing the influences of foil edge length, orbital load case, and material selection.