Journal articles: 'Geometrically nonlinear static analyses'

1

Yang, Lan, Changchuan Xie, and Chao Yang. "Geometrically exact vortex lattice and panel methods in static aeroelasticity of very flexible wing." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 3 (November 20, 2019): 742–59. http://dx.doi.org/10.1177/0954410019885238.

Full text

Abstract:

Geometrically exact vortex lattice method and panel method are presented in this paper to deal with aerodynamic load computation for geometrically nonlinear static aeroelastic problems. They are combined with geometrically nonlinear finite element method through surface spline interpolation in the loosely-coupled iteration. From the perspective of theoretical research, both vortex lattice method and panel method are based on the full potential equation and able to model the deflection and twist of the wing, while vortex lattice method is based on the thin airfoil theory, and panel method is suitable for thick wings. Although the potential flow equation is linear, the introduction of geometrically exact boundary conditions makes it significantly different from the linear aeroelastic analysis. The numerical results of a high aspect ratio wing are provided to declare the influence of large deformation on nonlinear static aeroelastic computation compared with linear analysis. Aeroelastic analyses based on geometrically exact vortex lattice method and panel method are also compared with the results of computational fluid dynamics/computational structural dynamics coupling method and the wind tunnel test data. The nonlinear static aeroelastic analysis agrees with the measurement even in considerably large deformation situations.

APA, Harvard, Vancouver, ISO, and other styles

2

Xenidis, Haris, Konstantinos Morfidis, and Panagis G. Papadopoulos. "Simple Nonlinear Static Analysis Using Truss Models for Modeling Snap-through of Thin Shallow Arches." Applied Mechanics and Materials 215-216 (November 2012): 685–91. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.685.

Full text

Abstract:

In this paper, a truss model is used for the geometrically nonlinear static analysis of a thin shallow arch subject to snap-through. Thanks to the very simple geometry of a truss, the equilibrium conditions can be easily written and the global stiffness matrix can be easily updated with respect to the deformed structure, within each step of the analysis. A very coarse discretization is applied. For the geometrically nonlinear static analysis, a short computer program has been developed by displacement control of a plane truss model of a structure. This very short, fully documented computer program is applied on the geometrically nonlinear static analysis of a specific thin shallow arch subject to snap-through.

APA, Harvard, Vancouver, ISO, and other styles

3

Kato, Shiro, Takashi Ueki, and Yoichi Mukaiyama. "Study of Dynamic Collapse of Single Layer Reticular Domes Subjected to Earthquake Motion and the Estimation of Statically Equivalent Seismic Forces." International Journal of Space Structures 12, no. 3-4 (September 1997): 191–203. http://dx.doi.org/10.1177/026635119701200308.

Full text

Abstract:

The present paper investigates the dynamic response characteristics of single layer reticular domes subjected to horizontal earthquake motions from the following view points: (1) how to estimate the statically equivalent seismic forces applied to domes both for high rise and low rise; and (2) how to estimate the collapse accelerations under which the domes collapse dynamically. For these purposes, linear response analyses, linear buckling analyses, geometrically and materially nonlinear static analyses and geometrically and materially nonlinear earthquake response analyses are performed. Based on the results, the collapse accelerations are expressed as a function of the safety factor for domes under self weight. The expression for the collapse accelerations leads to an approximate measure by which structural designers may balance the static resistant capacity under self weight and the dynamic resistant capacity under earthquake motions.

APA, Harvard, Vancouver, ISO, and other styles

4

Tsushima, Natsuki, Masato Tamayama, and Tomohiro Yokozeki. "Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis." JOURNAL OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 68, no. 4 (2020): 142–47. http://dx.doi.org/10.2322/jjsass.68.142.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Zuo, Wenjie, Ke Huang, and Fei Cheng. "EFESTS: Educational finite element software for truss structure – Part 3: Geometrically nonlinear static analysis." International Journal of Mechanical Engineering Education 45, no. 2 (February 20, 2017): 154–69. http://dx.doi.org/10.1177/0306419016689503.

Full text

Abstract:

This article covers the modeling, formulation, solution, and software development of the geometrically nonlinear static finite element method of truss structure. Firstly, we summarize the total Lagrange bar elment formulation, which includes the tangent stiffness matrix and the internal force vector. Secondly, static class diagrams and dynamic sequence diagrams assist students in designing software architecture. Thirdly, the analytical example of the 2-bar truss structure and the numerical example of the 10-bar truss structure are presented to promote students’ understanding of geometrically nonlinear finite element theory and application. Finally, the developed software is free for educational research and can be downloaded from the website: http://mach.jlu.edu.cn/hb_images/xygk/xssz_sz_js.php?id=395 .

APA, Harvard, Vancouver, ISO, and other styles

6

Sautter, Klaus Bernd, and Kai-Uwe Bletzinger. "Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS." Advances in Civil Engineering 2022 (December 1, 2022): 1–19. http://dx.doi.org/10.1155/2022/3573608.

Full text

Abstract:

Direct usage of construction plans as input for structural analyses assumes the reference configuration to match the engineering drawings. However, the built construction is typically supposed to match the construction plans after its successful erection. In that state, the structure is usually already subjected to self-weight and maybe other loadings. Consequently, an analysis approach is necessary to find the unknown reference configuration for a given, desired deformed structural shape. The standard static problem needs to be reformulated with the reference coordinates being the unknown variables. This work describes the necessary steps for geometrically and materially nonlinear truss elements based on the variation of reference strategy (VaReS) and gives a highly detailed description of all resultant system derivatives. Arbitrary hyperelastic material laws can be applied of which this work introduces the St. Venant-Kirchhoff, the Neo-Hookean, and the Ogden law. Additionally, the self-weight load case is considered, increasing the problem’s nonlinearity. Finally, two- and three-dimensional structural problems are presented to show the solution capabilities, ranging from simple 3-bar systems to larger framework bridges. While all necessary vectors and matrices are discussed and presented in great detail, a publicly available GitHub repository makes the code freely accessible as Python code.

APA, Harvard, Vancouver, ISO, and other styles

7

Upadhyay, A. K., and K. K. Shukla. "Geometrically nonlinear static and dynamic analysis of functionally graded skew plates." Communications in Nonlinear Science and Numerical Simulation 18, no. 8 (August 2013): 2252–79. http://dx.doi.org/10.1016/j.cnsns.2012.12.034.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Akbaş, Şeref Doğuşcan. "Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/871815.

Full text

Abstract:

Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM) subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

APA, Harvard, Vancouver, ISO, and other styles

9

Park, Kyusic, and Matthew S. Allen. "Quasi-static modal analysis for reduced order modeling of geometrically nonlinear structures." Journal of Sound and Vibration 502 (June 2021): 116076. http://dx.doi.org/10.1016/j.jsv.2021.116076.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Berry, D. T., and T. Y. Yang. "Simplified lattice beam elements for geometrically nonlinear static,dynamic, and postbuckling analysis." AIAA Journal 24, no. 8 (August 1986): 1346–47. http://dx.doi.org/10.2514/3.9441.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Tsushima, Natsuki, Tomohiro Yokozeki, Weihua Su, and Hitoshi Arizono. "Geometrically nonlinear static aeroelastic analysis of composite morphing wing with corrugated structures." Aerospace Science and Technology 88 (May 2019): 244–57. http://dx.doi.org/10.1016/j.ast.2019.03.025.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Behjat, B., and M. R. Khoshravan. "Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates." Composite Structures 94, no. 3 (February 2012): 874–82. http://dx.doi.org/10.1016/j.compstruct.2011.08.024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

CİVALEK, ÖMER. "LARGE DEFLECTION STATIC AND DYNAMIC ANALYSIS OF THIN CIRCULAR PLATES RESTING ON TWO-PARAMETER ELASTIC FOUNDATION: HDQ/FD COUPLED METHODOLOGY APPROACHES." International Journal of Computational Methods 02, no. 02 (June 2005): 271–91. http://dx.doi.org/10.1142/s0219876205000478.

Full text

Abstract:

An analysis of the geometrically nonlinear dynamics of thin circular plates on a two parameter elastic foundation is presented in this paper. The nonlinear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the harmonic differential quadrature method in the space domain and the finite difference numerical integration method in the time domain. Winkler-Pasternak foundation model is considered and the influence of stiffness of Winkler (K) and Pasternak (G) foundation on the geometrically nonlinear analysis of the circular plates has been investigated. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach. From the numerical computation, it can be concluded that the present coupled methodology is an efficient method for the nonlinear static and dynamic analysis of circular plates with or without an elastic medium.

APA, Harvard, Vancouver, ISO, and other styles

14

Wan, Ze-Qing, Shi-Rong Li, and Hong-Wei Ma. "Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures." Advances in Materials Science and Engineering 2019 (June 9, 2019): 1–10. http://dx.doi.org/10.1155/2019/6204145.

Full text

Abstract:

In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. The effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. This paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

APA, Harvard, Vancouver, ISO, and other styles

15

Misra, A., K. Behdinan, and W. L. Cleghorn. "IMPLEMENTATION OF CONSISTENT UPDATED LAGRANGIAN FORMULATION FOR STATIC ANALYSIS OF GEOMETRICALLY NONLINEAR BEAM." Transactions of the Canadian Society for Mechanical Engineering 24, no. 1B (May 2000): 135–42. http://dx.doi.org/10.1139/tcsme-2000-0009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Lai, Steven H. Y. "Geometrically nonlinear transient analysis of a rotating beam structure carrying a static payload." Mechanics Research Communications 21, no. 5 (September 1994): 473–82. http://dx.doi.org/10.1016/0093-6413(94)90041-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Agapov, Vladimir. "Realization of reinforced concrete structures analysis with the account of physical and geometrical nonlinearity in computer program PRINS." MATEC Web of Conferences 251 (2018): 04035. http://dx.doi.org/10.1051/matecconf/201825104035.

Full text

Abstract:

An algorithm of physically and geometrically nonlinear static analysis of structures by the finite element method is described, the distinguishing feature of which is the use of a full nonlinear stiffness matrix. This matrix is represented as the sum of five terms, namely, the stiffness matrix of the zero, first and second order, as well as matrices of initial displacements and initial stresses. When using modified Lagrange coordinates, the matrix of the initial displacements becomes a zero matrix. The calculation is carried out by a step-by-step method. Features of the application of this technique in the calculation of reinforced concrete structures are considered. The examples of static nonlinear analysis of reinforced concrete structures with the aid of program PRINS are given.

APA, Harvard, Vancouver, ISO, and other styles

18

Xie, Changchuan, Yi Liu, Chao Yang, and J. E. Cooper. "Geometrically Nonlinear Aeroelastic Stability Analysis and Wind Tunnel Test Validation of a Very Flexible Wing." Shock and Vibration 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/5090719.

Full text

Abstract:

VFAs (very flexible aircraft) have begun to attract significant attention because of their good flight performances and significant application potentials; however, they also bring some challenges to researchers due to their unusual lightweight designs and large elastic deformations. A framework for the geometrically nonlinear aeroelastic stability analysis of very flexible wings is constructed in this paper to illustrate the unique aeroelastic characteristics and convenient use of these designs in engineering analysis. The nonlinear aeroelastic analysis model includes the geometrically nonlinear structure finite elements and steady and unsteady nonplanar aerodynamic computations (i.e., the nonplanar vortex lattice method and nonplanar doublet-lattice method). Fully nonlinear methods are used to analyse static aeroelastic features, and linearized structural dynamic equations are established at the structural nonlinear equilibrium state to estimate the stability of the system through the quasimode of the stressed and deformed structure. The exact flutter boundary is searched via an iterative procedure. A wind tunnel test is conducted to validate this theoretical analysis framework, and reasonable agreement is obtained. Both the analysis and test results indicate that the geometric nonlinearity of very flexible wings presents significantly different aeroelastic characteristics under different load cases with large deformations.

APA, Harvard, Vancouver, ISO, and other styles

19

Beni, Y. T. "A Nonlinear Electro-Mechanical Analysis of Nanobeams Based on the Size-Dependent Piezoelectricity Theory." Journal of Mechanics 33, no. 3 (July 11, 2016): 289–301. http://dx.doi.org/10.1017/jmech.2016.65.

Full text

Abstract:

AbstractNonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on consistent size-dependent piezoelectricity theory. By considering geometrically nonlinear and axial displacement of the centroid of beam sections, basic nonlinear equations of piezoelectric nanobeam are derived using Hamilton's principle and variational method. Afterwards, in the special case for the formulation derived, hinged-hinged piezoelectric nanobeam is studied, and static deflection as well as free vibrations of the nanobeam under mechanical loads is determined. In this case, results of the linear formulation of the size-dependent theory are compared to those of the linear and nonlinear classical continuum theory.

APA, Harvard, Vancouver, ISO, and other styles

20

Bellora, Davide, and Riccardo Vescovini. "A Continuation Procedure for the Quasi-Static Analysis of Materially and Geometrically Nonlinear Structural Problems." Mathematical and Computational Applications 24, no. 4 (November 2, 2019): 94. http://dx.doi.org/10.3390/mca24040094.

Full text

Abstract:

Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material response. The main advantage of the proposed approach relies in its robustness, which can be exploited for tracing the equilibrium paths for problems characterized by complex responses involving the onset and propagation of cracks. A set of examples is presented and discussed. For problems involving combined material and geometric nonlinearties, the results illustrate the advantages of the proposed hybrid continuation technique in terms of efficiency and robustness. Specifically, less iterations are usually required with respect to similar procedures based on purely geometric constraints. Furthermore, bifurcation plots can be easily traced, furnishing the analyst a powerful tool for investigating the nonlinear response of the structure at hand.

APA, Harvard, Vancouver, ISO, and other styles

21

Soldatos, Kostas P. "Mechanics of Cylindrical Shells With Non-Circular Cross-Section: A Survey." Applied Mechanics Reviews 52, no. 8 (August 1, 1999): 237–74. http://dx.doi.org/10.1115/1.3098937.

Full text

Abstract:

This article presents a review of the research work related to the mechanical behavior of non-circular cylindrical shells and shell segments. To this end, after a brief reference to the basic nomenclature that is mainly used, it initially provides quite a general framework for most of the relevant governing equations employed in the relevant literature. It proceeds with a review of the corresponding dynamic analyses, which are primarily grouped according to the geometrical configuration of the noncircular shell considered and secondarily according to the type of the mathematical model employed. These deal with the dynamics of closed cylindrical shells and open cylindrical panels based on classical (CST) or transverse shear deformable shell theories (SDST). The static analyses reviewed next are divided according to the nature of the physical problem considered and deal with small as well as with large deflections of statically loaded non-circular cylindrical shells. These include both linearized and geometrically nonlinear elastic stability analyses as well as the very few relevant studies that assumed an elastic-plastic response of the shell material constitution. This review article contains 196 references.

APA, Harvard, Vancouver, ISO, and other styles

22

Chen, Xi, Ying Liu, and Hua Zhang. "Finite Element Analysis of Different Flexure Springs." Applied Mechanics and Materials 44-47 (December 2010): 2065–69. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.2065.

Full text

Abstract:

Flexure spring suspensions have demonstrated the ability to provide long operating lifetimes for cryocoolers. The good flexure spring need high radial stiffness and high fatigue life. The profile curves are very important for flexure spring. In this paper, based on the finite element analysis software (ANSYS), geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis were made to several different flexure springs. The fatigue strength, axial and radial stiffness, modal frequency were calculated and listed. The different performance between linear flexure spring and spiral flexure spring were discussed, which would provide an advisory opinion for the design and application of flexure spring in space cryocooler.

APA, Harvard, Vancouver, ISO, and other styles

23

Krivenko, Olga, Grygorii Ivanchenko, Yurii Vorona, and Iryna Kara. "GEOMETRICALLY NONLINEAR DEFORMATION AND BUCKLING OF SMOOTH AND FACETED SHELLS." Management of Development of Complex Systems, no. 48 (December 20, 2021): 69–74. http://dx.doi.org/10.32347/2412-9933.2021.48.69-74.

Full text

Abstract:

Practical using of curvilinear shape shells is related with significant problems during their production especially for metal structures. Therefore during such shells production curvilinear shape is replaced by faceted. Realization of this method when designing needs additional investigations performing of faceted shells bearing capacity on the basis of appropriate numerical calculation method using. Problems of solving such tasks are practically not displayed in the literature. Break-in of the middle surface affect significantly to the shell stress-strain state. Accounting of temperature fields’ influence in the problems of their stability complicates their behavior research even more. In this paper the research results comparing analysis of static problems about smooth and faceted shells nonlinear deformation and stability under mechanical loads is presented. The problem is solving with using of software that are based on the finite element method: by method that realized the moment finite-element scheme and using software package LIRA. The solving method that used the moment finite-element scheme is based on the geometrically nonlinear equations of the 3D theory of thermoelasticity without application of theory of shells simplifying hypothesis and on the applications of the universal three-dimensional solid finite element.

APA, Harvard, Vancouver, ISO, and other styles

24

Chen, Lidao, Xin Hu, and Yong Liu. "Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam." Aerospace 10, no. 2 (January 17, 2023): 92. http://dx.doi.org/10.3390/aerospace10020092.

Full text

Abstract:

In this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time and space. Therefore, it is natural to discretize it in time and space simultaneously. Considering the continuity and intrinsic boundary conditions in the spatial direction and the continuity and periodic boundary conditions in the time direction, the boundary value scheme of space-time finite element for solving the full intrinsic equations is derived. This method has been successfully applied to the static analysis and dynamic response solution of the fully intrinsic equations of nonlinear geometrically exact beam. The numerical results of several examples are compared with the analytical solution, existing algorithms, and literature to illustrate the applicability, accuracy and efficiency of this method.

APA, Harvard, Vancouver, ISO, and other styles

25

Isoldi, Liércio André, Armando Miguel Awruch, Paulo Roberto de F. Teixeira, and Inácio B. Morsch. "Geometrically nonlinear static and dynamic analysis of composite laminates shells with a triangular finite element." Journal of the Brazilian Society of Mechanical Sciences and Engineering 30, no. 1 (March 2008): 84–93. http://dx.doi.org/10.1590/s1678-58782008000100012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Shivakumar, J., M. H. Ashok, and Vishwanath Khadakbhavi. "Performance analysis of geometrically nonlinear static deformations of laminated composite plates using PFRC/AFC materials." Materials Today: Proceedings 5, no. 13 (2018): 27254–59. http://dx.doi.org/10.1016/j.matpr.2018.09.041.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Heidari, Mohammad, Ali Heidari, and Hadi Homaei. "Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory." Computational Intelligence and Neuroscience 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/571632.

Full text

Abstract:

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.

APA, Harvard, Vancouver, ISO, and other styles

28

Hui, Y., G. De Pietro, G. Giunta, S. Belouettar, H. Hu, E. Carrera, and A. Pagani. "Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements." Mathematical Problems in Engineering 2018 (November 27, 2018): 1–22. http://dx.doi.org/10.1155/2018/4821385.

Full text

Abstract:

The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

APA, Harvard, Vancouver, ISO, and other styles

29

Sapountzakis, Evangelos J. "Bars under Torsional Loading: A Generalized Beam Theory Approach." ISRN Civil Engineering 2013 (March 21, 2013): 1–39. http://dx.doi.org/10.1155/2013/916581.

Full text

Abstract:

In this paper both the static and dynamic analyses of the geometrically linear or nonlinear, elastic or elastoplastic nonuniform torsion problems of bars of constant or variable arbitrary cross section are presented together with the corresponding research efforts and the conclusions drawn from examined cases with great practical interest. In the presented analyses, the bar is subjected to arbitrarily distributed or concentrated twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. For the dynamic problems, a distributed mass model system is employed taking into account the warping inertia. The analysis of the aforementioned problems is complete by presenting the evaluation of the torsion and warping constants of the bar, its displacement field, its stress resultants together with the torsional shear stresses and the warping normal and shear stresses at any internal point of the bar. Moreover, the construction of the stiffness matrix and the corresponding nodal load vector of a bar of arbitrary cross section taking into account warping effects are presented for the development of a beam element for static and dynamic analyses. Having in mind the disadvantages of the 3D FEM solutions, the importance of the presented beamlike analyses becomes more evident.

APA, Harvard, Vancouver, ISO, and other styles

30

Ma, Baoshun, Jia Lu, Robert E. Harbaugh, and Madhavan L. Raghavan. "Nonlinear Anisotropic Stress Analysis of Anatomically Realistic Cerebral Aneurysms." Journal of Biomechanical Engineering 129, no. 1 (July 21, 2006): 88–96. http://dx.doi.org/10.1115/1.2401187.

Full text

Abstract:

Background. Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. Method of Approach. The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100mmHg. Results. The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30MPa in a small aneurysm to as high as 1.06MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. Conclusions. A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm rupture.

APA, Harvard, Vancouver, ISO, and other styles

31

Krivenko, Olha, Yurii Vorona, and Andrii Kozak. "Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures." Strength of Materials and Theory of Structures, no. 107 (October 29, 2021): 20–34. http://dx.doi.org/10.32347/2410-2547.2021.107.20-34.

Full text

Abstract:

Thin-walled shell-type structures are widely used in various branches of technology and industry. Such structures under operating conditions are usually exposed to various loads, including thermomechanical ones. Real shell structures, as a rule, have a complex shapes. To increase reliability, reduce material consumption, for technological reasons, they are designed as inhomogeneous systems in thickness. This causes a great and constant interest of engineers and designers in the problems of investigating the behavior of elastic thin-walled shell structures. The work is devoted to the method of analysis of geometrically nonlinear deformation, stability, post-buckling behavior and natural vibrations of thin elastic shells of complex shape and structure under the action of static thermomechanical loads. The unified design model has been created on the basis of the developed universal spatial finite element with introduced additional variable parameters. The model takes into account the multilayer material structure and geometric features for structural elements of the thin shell. The shells can be reinforced with ribs and cover plates, weakened by cavities, channels and holes, have sharp bends in the mid-surface. Such a uniform formulation made it possible to create a unified finite element model of the shells with an inhomogeneous structure. It is shown on a number of problems that the method presented in this article is an effective tool for analyzing geometrically nonlinear deformation, stability, post-buckling behavior and natural vibrations of thin elastic shells of an inhomogeneous structure under the action of static thermomechanical loads.

APA, Harvard, Vancouver, ISO, and other styles

32

Xie, Changchuan, Yang Meng, Fei Wang, and Zhiqiang Wan. "Aeroelastic Optimization Design for High-Aspect-Ratio Wings with Large Deformation." Shock and Vibration 2017 (2017): 1–16. http://dx.doi.org/10.1155/2017/2564314.

Full text

Abstract:

This paper presents a framework of aeroelastic optimization design for high-aspect-ratio wing with large deformation. A highly flexible wing model for wind tunnel test is optimized subjected to multiple aeroelastic constraints. Static aeroelastic analysis is carried out for the beamlike wing model, using a geometrically nonlinear beam formulation coupled with the nonplanar vortex lattice method. The flutter solutions are obtained using the P-K method based on the static equilibrium configuration. The corresponding unsteady aerodynamic forces are calculated by nonplanar doublet-lattice method. This paper obtains linear and nonlinear aeroelastic optimum results, respectively, by the ISIGHT optimization platform. In this optimization problem, parameters of beam cross section are chosen as the design variables to satisfy the displacement, flutter, and strength requirements, while minimizing wing weight. The results indicate that it is necessary to consider geometrical nonlinearity in aeroelastic optimization design. In addition, optimization strategies are explored to simplify the complex optimization process and reduce the computing time. Different criterion values are selected and studied for judging the effects of the simplified method on the computing time and the accuracy of results. In this way, the computing time is reduced by more than 30% on the premise of ensuring the accuracy.

APA, Harvard, Vancouver, ISO, and other styles

33

Wu, Chih-Ping, Zong-Li Hong, and Yung-Ming Wang. "Geometrically Nonlinear Static Analysis of an Embedded Multiwalled Carbon Nanotube and the van der Waals Interaction." Journal of Nanomechanics and Micromechanics 7, no. 4 (December 2017): 04017012. http://dx.doi.org/10.1061/(asce)nm.2153-5477.0000134.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Civalek, Ö. "Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations." International Journal of Pressure Vessels and Piping 113 (January 2014): 1–9. http://dx.doi.org/10.1016/j.ijpvp.2013.10.014.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Lohar, Hareram, Anirban Mitra, and Sarmila Sahoo. "Mode switching phenomenon in geometrically nonlinear free vibration analysis of in-plane inhomogeneous plates on elastic foundation." Curved and Layered Structures 5, no. 1 (July 1, 2018): 156–79. http://dx.doi.org/10.1515/cls-2018-0012.

Full text

Abstract:

Abstract Effect of geometric nonlinearity onfree vibration behaviour of a non-uniform in-plane inhomogeneousplate on elastic foundation is carried out with an emphasis on mode switching phenomenon. The formulation is semianalytic displacement based and it is carried out in two distinct steps. First, the static problem is solved to find out the unknown displacement field by using minimum total potential energy principle. Secondly, subsequent dynamic problem is set up as an eigenvalue problem on the basis of the known displacement field. The governing set of equations in dynamic problem is obtained by using Hamilton’s principle. In static analysis, unknown co-efficient of the governing equations are solved using an iterative method, which is direct substitution with relaxation method. The dynamic problem is solved with the help of intrinsic Matlab solver. The results of the present method are validated with existing data. Backbone curve corresponding to different combinations of systemparameters are presented in non-dimensional plane.Mode switching is observed to occur in certain specific situation. The linear and nonlinear mode shapes are also furnished to support the presence of switching phenomenon.

APA, Harvard, Vancouver, ISO, and other styles

36

Filippi, Matteo, Alfonso Pagani, and Erasmo Carrera. "Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements." Journal of the American Helicopter Society 64, no. 3 (July 1, 2019): 1–10. http://dx.doi.org/10.4050/jahs.64.032005.

Full text

Abstract:

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

APA, Harvard, Vancouver, ISO, and other styles

37

Van Damme, Christopher, Alecio Madrid, Matthew Allen, and Joseph Hollkamp. "Simultaneous Regression and Selection in Nonlinear Modal Model Identification." Vibration 4, no. 1 (March 13, 2021): 232–47. http://dx.doi.org/10.3390/vibration4010016.

Full text

Abstract:

High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions.

APA, Harvard, Vancouver, ISO, and other styles

38

Yoo, W. S., and E. J. Haug. "Dynamics of Flexible Mechanical Systems Using Vibration and Static Correction Modes." Journal of Mechanisms, Transmissions, and Automation in Design 108, no. 3 (September 1, 1986): 315–22. http://dx.doi.org/10.1115/1.3258733.

Full text

Abstract:

A finite-element-based method is developed and applied for geometrically nonlinear dynamic analysis of spatial mechanical systems. Vibration and static correction modes are used to account for linear elastic deformation of components. Boundary conditions for vibration and static correction mode analysis are defined by kinematic constraints between components of a system. Constraint equations between flexible bodies are derived and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A standard, lumped mass finite-element structural analysis code is used to generate deformation modes and deformable body mass and stiffness information. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled effects of geometric nonlinearity and elastic deformation. Two examples are presented and the effects of deformation mode selection on dynamic prediction are analyzed.

APA, Harvard, Vancouver, ISO, and other styles

39

Foroutan, Kamran, and Habib Ahmadi. "Nonlinear Static and Dynamic Buckling Analyses of Imperfect FGP Cylindrical Shells Resting on Nonlinear Elastic Foundation Under Axial Compression." International Journal of Structural Stability and Dynamics 20, no. 07 (July 2020): 2050074. http://dx.doi.org/10.1142/s0219455420500741.

Full text

Abstract:

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

APA, Harvard, Vancouver, ISO, and other styles

40

Luo, Dan, Yifeng Zhong, Boshu Li, and Bin Deng. "Static and dynamic analysis of composite box beam based on geometrically exact nonlinear model considering non-classical effects." Composite Structures 204 (November 2018): 689–700. http://dx.doi.org/10.1016/j.compstruct.2018.07.127.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Lohar, Hareram, Anirban Mitra, and Sarmila Sahoo. "Geometrically Non-Linear Frequency Response of Axially Functionally Graded Beams Resting on Elastic Foundation Under Harmonic Excitation." International Journal of Manufacturing, Materials, and Mechanical Engineering 8, no. 3 (July 2018): 23–43. http://dx.doi.org/10.4018/ijmmme.2018070103.

Full text

Abstract:

This article presents geometrically nonlinear forced vibration analysis of an axially functionally graded (AFG) non-uniform beam resting on an elastic foundation. The mathematical formulation is displacement based and derivation of governing equations is accomplished following Hamilton's principle. The foundation has been mathematically incorporated into the analysis as a set of linear springs. According to the basic assumption of the present method force equilibrium condition is satisfied at a maximum excitation amplitude value. Thus, the dynamic problem is equivalently represented as a static one, which is solved by following a numerical implementation of the Broyden method. It is a method that utilizes the Jacobian matrix and subsequent correction of the initial Jacobian to solve a system of nonlinear equations. The large amplitude dynamic behaviour of the system in terms of non-dimensional frequency response curves is validated against established results and new results are furnished for a parabolic tapered AFG beam on a linear elastic foundation.

APA, Harvard, Vancouver, ISO, and other styles

42

Elkaranshawy, Hesham A., Ahmed A. H. Elerian, and Walied I. Hussien. "A Corotational Formulation Based on Hamilton’s Principle for Geometrically Nonlinear Thin and Thick Planar Beams and Frames." Mathematical Problems in Engineering 2018 (August 14, 2018): 1–22. http://dx.doi.org/10.1155/2018/2670462.

Full text

Abstract:

A corotational finite element formulation for two-dimensional beam elements with geometrically nonlinear behavior is presented. The formulation separates the rigid body motion from the pure deformation which is always small relative to the corotational element frame. The stiffness matrices and the mass matrices are evaluated using both Euler-Bernoulli and Timoshenko beam models to reveal the shear effect in thin and thick beams and frames. The nonlinear equilibrium equations are developed using Hamilton’s principle and are defined in the global coordinate system. A MATLAB code is developed for the numerical solution. In static analysis, the code employed an iterative method based on the full Newton-Raphson method without incremental loading, while, in dynamic analysis, the Newmark direct integration implicit method is also utilized. Several examples of flexible beams and frames with large displacements are presented. Not only is the method simple and time-saving, but it is also highly effective and highly accurate.

APA, Harvard, Vancouver, ISO, and other styles

43

Ivanov, Sergey P., Anastasia S. Ivanova, and Oleg G. Ivanov. "The stability of geometrically nonlinear plate systems under the action of dynamic loads." Structural Mechanics of Engineering Constructions and Buildings 16, no. 3 (December 15, 2020): 219–25. http://dx.doi.org/10.22363/1815-5235-2020-16-3-219-225.

Full text

Abstract:

Relevance. Single-connected and multi-connected plate systems are widely used in construction, aircraft, shipbuilding, mechanical engineering, instrument making. As a result, the study of the stability of geometrically nonlinear plate systems is an urgent topic. But, despite significant achievements in this area, there are still many unsolved problems. Thus, the requests of the above-mentioned areas of application of thin-walled spatial systems require further study of the issue of static and dynamic stability. The aim of the work - development of a method of the dynamic stability analysis of geometrically nonlinear plate systems such as prismatic shells under the action of dynamic compression loads. Methods. A plate system, which is subject to dynamic compression loads in the longitudinal direction, is considered. Kirchhoff - Love hypotheses are taken into account. The material stress-deformation diagram is linear. The displacement of points in the normal direction to the median plane of the plates is determined in the form of the Vlasov expansion. To derive the basic differential equations of stability, the energy method and the variational Vlasov method are used. The extreme value of the total energy is determined using the Euler - Lagrange equation. As a result, a set of basic nonlinear differential equations for studying the buckling of the plate system under the action of dynamic compression loads is obtained. Results. The developed method is used to stability analysis of a geometrically nonlinear prismatic shell with a closed contour of the cross section, under central compression under the action of dynamic loading. The edges of the shell rest on the diaphragm. The buckling of the prismatic shell in the longitudinal direction along one and two half-waves of a sinusoid is studied. The numerical integration of nonlinear differential equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the dependence of the relative deflection on the dynamic coefficient are constructed. The influence of the rate of change of compression stress, the initial imperfection of the system, and other parameters on the criteria for the dynamic stability of the plate system is investigated.

APA, Harvard, Vancouver, ISO, and other styles

44

Krivenko, Olha, and Yurii Vorona. "Comparative Analysis of Nonlinear Deformation and Buckling of Thin Elastic Shells of Step-Variable Thickness." Strength of Materials and Theory of Structures, no. 108 (May 30, 2022): 107–18. http://dx.doi.org/10.32347/2410-2547.2022.108.107-118.

Full text

Abstract:

A comparative analysis of finite element models and methods for solving complex problems of geometrically nonlinear deformation, buckling and post-buckling behavior of thin shells of stepwise variable thickness is carried out. An approach based on the use of the moment scheme of finite elements is considered. The features of using the software suite LIRA and integrated software system SCAD for solving the assigned problems are also provided. Thin and medium thickness shells are considered. They can have different geometric features in thickness and be under the action of static thermomechanical loads. A technique for solving these problems with the help of an efficient refined approach is presented. The technique is based on the general methodological positions of the three-dimensional theory of thermoelasticity and the use of the finite element moment scheme. With this approach, the approximation through the shell thickness is carried out by a single universal spatial finite element. The element can be modified in different portions of the shell with a step-variable thickness. It can be located eccentrically relative to the middle surface of the casing and can change its dimensions in the direction of the shell thickness. Such a unified approach made it possible to create a unified designed finite element model of a shell of an inhomogeneous geometric structure under the combined action of a thermomechanical load. A comparative analysis of the application of three finite element approaches for problems of geometrically nonlinear deformation and buckling of shells of stepwise variable thickness is carried out.

APA, Harvard, Vancouver, ISO, and other styles

45

Na, Y. H., J. H. Kim, and S. J. Shin. "Vibration analyses of an equivalent plate wing with an external store." Aeronautical Journal 118, no. 1207 (September 2014): 1090–98. http://dx.doi.org/10.1017/s0001924000009763.

Full text

Abstract:

Generally, pylon-mounted external stores significantly affect the aerodynamic characteristics of the aircraft due to their flexibility. Therefore, many investigations upon the dynamic and aeroelastic characteristics of an aircraft wing with external stores have been done over the last few decades Recently, a study was carried out regarding the aeroelastic effects on wings by the engine placement For severe operation conditions, classical linear theory with a small amount of amplitude vibration may not be an appropriate analysis. Nonlinear vibration analysis will be required, especially when the amplitude of the vibration is larger than the wing thickness. Chia performed static, dynamic, and post-buckling analyses of various isotropic and composite plates for that purpose. Dumir and Bhaskar derived finite element formulations to analyse the nonlinear vibration of beams and plates. Moreover, the variational-asymptotic plate formulation and the accompanying equations for the global analysis for the plates have been studied. That approach accounted every possible geometrical non-linearity associated with large displacement and small strain.

APA, Harvard, Vancouver, ISO, and other styles

46

Duarte Filho, Luiz A., and Armando M. Awruch. "Geometrically nonlinear static and dynamic analysis of shells and plates using the eight-node hexahedral element with one-point quadrature." Finite Elements in Analysis and Design 40, no. 11 (July 2004): 1297–315. http://dx.doi.org/10.1016/j.finel.2003.08.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Civalek, Ömer. "Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation." Journal of Sound and Vibration 294, no. 4-5 (July 2006): 966–80. http://dx.doi.org/10.1016/j.jsv.2005.12.041.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Heidari, Mohammad, Yaghoub Tadi Beni, and Hadi Homaei. "Estimation of Static Pull-In Instability Voltage of Geometrically Nonlinear Euler-Bernoulli Microbeam Based on Modified Couple Stress Theory by Artificial Neural Network Model." Advances in Artificial Neural Systems 2013 (December 26, 2013): 1–10. http://dx.doi.org/10.1155/2013/741896.

Full text

Abstract:

In this study, the static pull-in instability of beam-type micro-electromechanical system (MEMS) is theoretically investigated. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two supervised neural networks, namely, back propagation (BP) and radial basis function (RBF), have been used for modeling the static pull-in instability of microcantilever beam. These networks have four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data employed for training the networks and capabilities of the models in predicting the pull-in instability behavior has been verified. Based on verification errors, it is shown that the radial basis function of neural network is superior in this particular case and has the average errors of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations show a good agreement, which also proves the feasibility and effectiveness of the adopted approach.

APA, Harvard, Vancouver, ISO, and other styles

49

Karkauskas, Romanas, and Michail Popov. "THE ANALYSIS OF GEOMETRICALLY NONLINEAR ELASTIC-PLASTIC SPACE FRAMES / TAMPRIAI PLASTINIŲ GEOMETRIŠKAI NETIESINIŲ ERDVINIŲ RĖMŲ ANALIZĖ." Journal of Civil Engineering and Management 17, no. 4 (December 21, 2011): 558–68. http://dx.doi.org/10.3846/13923730.2011.602983.

Full text

Abstract:

The establishment of the real stress-strain state of the structure is one of the most important problems for designing and undertaking the reconstruction of building constructions as well as making calculations for the purpose of optimizing cross-sections of various structural elements. This task can be achieved by analysing the structure as a geometrically nonlinear system (refusing an assumption of small displacements) and taking into consideration plastic deformations. Modern computer technologies and mathematical tools enable us to perform strength analysis of space structures and to increase the accuracy of stress-strain state analysis. The present paper develops a technique for constructing a finite element tangent matrix for the nonlinear analysis of the space frame structure aimed at determining plastic deformations. The mathematical models of the problems based on static and kinematic formulations using the dual theory of mathematical programming were created for analysis. Strength conditions presented in construction codes and specifications AISCLRFD and suggested by other researchers (e.g. Orbison's strength conditions) are used in the formulations of the analysed problems. The mathematical models of the considered problems are tested by calculating a two-storied space frame. The results of the performed analysis are compared with data obtained within the studies conducted by other researchers. Santrauka Projektuojant ar rekonstruojant konstrukcijas, atliekant jos elementų skerspjūvių optimizavimo skaičiavimus, vienas iš svarbiausių uždavinių – konstrukcijos tikrojo įtempto deformuoto būvio (ĮDB) nustatymas. Tai galima pasiekti atliekant konstrukcijos kaip geometriškai netiesinės sistemos (atsisakant mažų poslinkių prielaidos) analizę, įvertinant plastines deformacijas. Taikant šiuolaikines kompiuterines technologijas ir matematinį aparatą, tapo įmanoma vykdyti erdvinės konstrukcijos stiprumo analizę ir padidinti konstrukcijos ĮDB analizės tikslumą. Tuo tikslu šiame darbe toliau plėtojama tangentinės standumo matricos sudarymo metodika erdvinės rėminės konstrukcijos netiesinei analizei, įvertinant plastines deformacijas. Naudojant matematinio programavimo dualumo teoriją sudaryti analizės statinės ir kinematinės formuluočių uždavinių matematiniai modeliai. Naudojamos AISC-LRFD normatyviniuose dokumentuose pateiktos ir kitų autorių (pavyzdžiui, Orbison) pasiūlytos stiprumo sąlygos. Suformuluoti analizės uždavinių matematiniai modeliai buvo aprobuoti skaičiuojant dviejų aukštų erdvinį rėmą. Gauti analizės rezultatai palyginti su eksperimentiniais ir kitų autorių analitiniais rezultatais.

APA, Harvard, Vancouver, ISO, and other styles

50

Chen, Wei, Ziyang Hu, Huliang Dai, and Lin Wang. "Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity." Applied Mathematics and Mechanics 41, no. 9 (June 30, 2020): 1381–400. http://dx.doi.org/10.1007/s10483-020-2646-6.

Full text

Abstract:

Abstract In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn, buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle. In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides, the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Geometrically nonlinear static analyses'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles