Статті в журналах: "Nonlinear geometrical analysi"

1

Yin, Shuohui, Tiantang Yu, Tinh Quoc Bui, and Minh Ngoc Nguyen. "Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis." Engineering Computations 32, no. 2 (April 20, 2015): 519–58. http://dx.doi.org/10.1108/ec-09-2013-0220.

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Purpose – The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs. Design/methodology/approach – A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents. Findings – The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized. Originality/value – This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.

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2

El Hantati, Issam, Ahmed Adri, Hatim Fakhreddine, Said Rifai, and Rhali Benamar. "Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams." Shock and Vibration 2022 (January 30, 2022): 1–22. http://dx.doi.org/10.1155/2022/8464255.

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In this study, the geometrically nonlinear free and forced vibrations of tapered beams are investigated on the basis of the Euler-Bernoulli beam theory and the von Karman geometric nonlinearity assumptions. The aim of the analysis is to determine tapered beams nonlinear frequencies and modes, and the associated stress distributions by means of bending moment diagrams. The linear problem is first solved. Then, to tackle the nonlinear problem, the displacement function is expanded as a series of the linear modes and the discrete expressions for the strain and kinetic energies are derived. Assuming a point excitation of the beam, the algebraic nonlinear system obtained based on Hamilton’s principle is solved by an approximate method. The effect of the geometric nonlinearity in both the free and forced cases was illustrated and discussed and the effect of the variation of various tapered beam geometrical parameters. The effect of varying the excitation level was also examined.

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3

ANCO, STEPHEN C. "GAUGE THEORY DEFORMATIONS AND NOVEL YANG–MILLS CHERN–SIMONS FIELD THEORIES WITH TORSION." International Journal of Geometric Methods in Modern Physics 01, no. 04 (August 2004): 493–544. http://dx.doi.org/10.1142/s0219887804000265.

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A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The physical interest in studying deformations is to address uniqueness of known nonlinear interactions of gauge fields and to look systematically for theoretical possibilities for new interactions. Mathematically, the study of deformations aims to understand the rigidity of the nonlinear structure of gauge field theories and to uncover new types of nonlinear geometrical structures. The first part of this paper summarizes and significantly elaborates a field-theoretic deformation method developed in earlier work. Some key contributions presented here are, firstly, that the determining equations for deformation terms are shown to have an elegant formulation using Lie derivatives in the jet space associated with the gauge field variables. Secondly, the obstructions (integrability conditions) that must be satisfied by lowest-order deformations terms for existence of a deformation to higher orders are explicitly identified. Most importantly, a universal geometrical structure common to a large class of nonlinear gauge theory examples is uncovered. This structure is derived geometrically from the deformed gauge symmetry and is characterized by a covariant derivative operator plus a nonlinear field strength, related through the curvature of the covariant derivative. The scope of these results encompasses Yang–Mills theory, Freedman–Townsend theory, and Einstein gravity theory, in addition to their many interesting types of novel generalizations that have been found in the past several years. The second part of the paper presents a new geometrical type of Yang–Mills generalization in three dimensions motivated from considering torsion in the context of nonlinear sigma models with Lie group targets (chiral theories). The generalization is derived by a deformation analysis of linear abelian Yang–Mills Chern–Simons gauge theory. Torsion is introduced geometrically through a duality with chiral models obtained from the chiral field form of self-dual (2+2) dimensional Yang–Mills theory under reduction to (2+1) dimensions. Field-theoretic and geometric features of the resulting nonlinear gauge theories with torsion are discussed.

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4

Nie, G. J., and Zheng Zhong. "The Elasto-Plastic and Geometrically Nonlinear Finite Element Model of Space Beam Considering Restraint Torsion." Key Engineering Materials 340-341 (June 2007): 335–40. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.335.

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A new elasto-plastic and geometrically nonlinear finite element model of space beam considering restraint torsion and the coupling effect of deformations is presented in this paper. The warping restraint torsion and the coupling effect of deformation are considered in the displacement formulation of arbitrary point on the space beam. The geometrical relationship of arbitrary point is derived according to the definition of Green strain. The elasto-plastic and geometrically nonlinear finite element model of space beam is derived using Updated Lagrange description. The effect of axial force, shearing force, biaxial bending moment, moment of torsion and bimoment is involved in the geometrical stiffness matrix of element. The yielding developments both across the section and along the axis of the member are taken into consideration by selecting Gauss points. The full historical nonlinear analysis is achieved using the method of load increment and modified Newton-Raphson method. The validity of the new model derived in this paper is proved by numerical example. This new model can be used in the elasto-plastic and geometrically nonlinear analysis of space beam structures constructed by the members of arbitrary cross section.

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5

BUENO, J. R., and D. D. LORIGGIO. "Analysis of second order effects: case study." Revista IBRACON de Estruturas e Materiais 9, no. 4 (August 2016): 494–501. http://dx.doi.org/10.1590/s1983-41952016000400002.

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Abstract This paper presents a nonlinear static analysis of a reinforced concrete plane frame. It has as main objective is to realize a global stability verification of a plane frame, by using geometric stiffness matrix. In order to obtain first and second order combined effects, equilibrium and kinematic relations were studied in the deformed geometric configuration. These results were obtained by using geometric stiffness matrix and multiplying horizontal forces by Gamma-Z coefficient. Both procedures disclosed very similar results in the study, indicating that Gamma-Z can be used to study equilibrium and kinematic relations in deformed geometrical configuration of the structure.

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6

Xu, R., D. X. Li, J. P. Jiang, and W. Liu. "Nonlinear Vibration Analysis of Membrane SAR Antenna Structure Adopting a Vector Form Intrinsic Finite Element." Journal of Mechanics 31, no. 3 (January 23, 2015): 269–77. http://dx.doi.org/10.1017/jmech.2014.97.

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ABSTRACTThis study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to study the nonlinear vibration of the membrane SAR (Synthetic Aperture Radar) antenna structure. As the dynamic characteristic of the antenna is mainly determined by the support frame, it can be simplified as an axially loaded cantilever beam. The linear and geometrically nonlinear models of the axially loaded cantilever beam are established. The beam is modeled as discrete mass points which are connected by deformable elements through VFIFE method. A statics analysis is first presented to verify the VFIFE method. Then effects of the geometrical nonlinearity and axial load are investigated. It is believed that the presented study is valuable for better understanding the influences of the geometrical nonlinearity and axial load of the cantilever beam on the structural vibration characteristics.

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7

Liu, Mu Yu, and Feng Wang. "Geometrically Nonlinear Analysis of Long Span Composite Girder Cable-Stayed Bridge with Three Towers under Live Load." Applied Mechanics and Materials 34-35 (October 2010): 371–75. http://dx.doi.org/10.4028/www.scientific.net/amm.34-35.371.

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A comparison on geometrically nonlinear analysis of composite girder cable-stayed bridge is presented. The spatial nonlinear analysis model named double-girder is established, the geometrically nonlinear behavior of whole bridge is analyzed under dead load plus live load in normal service stage, the nonlinear analysis involves cable sag, large displacement and beam-column, the three nonlinear factors effect on internal force and deformation of side tower, main girder are investigated. The results show that the effect of geometric nonlinearity is small on bending moment and deformation of side tower, and also small on vertical deflection of main girders, but nonlinear effect is large on bending moment of main girders. Results obtained in this research and conclusions made provide valuable insight and guidelines for the design of composite girder cable-stayed bridge with three towers.

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8

Pavlos, G. P., M. A. Athanasiu, D. Kugiumtzis, N. Hatzigeorgiu, A. G. Rigas, and E. T. Sarris. "Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data." Nonlinear Processes in Geophysics 6, no. 1 (March 31, 1999): 51–65. http://dx.doi.org/10.5194/npg-6-51-1999.

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Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

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9

GU, Y. T. "GEOMETRICALLY NONLINEAR ANALYSIS OF MICROSWITCHES USING THE LOCAL MESHFREE METHOD." International Journal of Computational Methods 05, no. 04 (December 2008): 513–32. http://dx.doi.org/10.1142/s0219876208001601.

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In the modeling and simulation of microelectromechanical system (MEMS) devices, such as the microswitch, the large deformation or the geometrical nonlinearity should be considered. Due to the issue of mesh distortion, the finite element method (FEM) is not effective for this large deformation analysis. In this paper, a local meshfree formulation is developed for geometrically nonlinear analysis of MEMS devices. The moving least squares approximation (MLSA) is employed to construct the meshfree shape functions based on the arbitrarily distributed field nodes and the spline weight function. The discrete system of equations for two-dimensional MEMS analysis is obtained using the weighted local weak form, and based on the total Lagrangian (TL) approach, which refers all variables to the initial configuration. The Newton–Raphson iteration technique is used to get the final results. Several typical microswitches are simulated by the developed nonlinear local meshfree method. Some important parameters of these microswitches, e.g. the pull-in voltage, are studied. Compared with the experimental results and results obtained by linear analysis, nonlinear meshfree analysis of microswitches is accurate and efficient. It has demonstrated that the present nonlinear local meshfree formulation is very effective for geometrically nonlinear analysis of MEMS devices, because it totally avoids the issue of mesh distortion in the FEM.

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10

Karad, P. B., and P. V. Patel. "Geometric Nonlinear Analysis of RC Frame structure using Applied Element Method (AEM)." Proceedings of the 12th Structural Engineering Convention, SEC 2022: Themes 1-2 1, no. 1 (December 19, 2022): 245–50. http://dx.doi.org/10.38208/acp.v1.504.

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Reinforced Concrete (RC) structural elements having vast varieties of applications. Understanding the failure mechanism, deflection capacity beyond elastic limit is very important from the structural engineering point of view. Various RC structures are slender in nature which produces large deformations due to geometric nonlinearity. Nonlinear analysis of RC structures is very complex in nature and hence there is need of highly efficient numerical method. Applied Element Method (AEM) is a displacement-based method which can track highly nonlinear behavior of the structure i.e. crack initiation and propagation, element separation, rigid body motion of structural elements and total collapse process with the high accuracy. In this study, the aim of the geometrical nonlinear analysis is to predict the deflection of the RC structure at various loading interval. In this paper the results obtained using AEM are compared with the Finite Element Method (FEM) based results obtained using the ABAQUS software. It is observed that there is a close agreement between the results obtained using AEM and FEM which shows that, AEM can be used for the geometric nonlinear analysis of the structures effectively.

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11

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.

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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.

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12

Li, Zhao Kun, Hua Mei Bian, Li Juan Shi, and Xiao Tie Niu. "Reliability-Based Topology Optimization of Compliant Mechanisms with Geometrically Nonlinearity." Applied Mechanics and Materials 556-562 (May 2014): 4422–34. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4422.

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A new reliability-based topology optimization method for compliant mechanisms with geometrical nonlinearity is presented. The aim of this paper is to integrate reliability and geometrical nonlinear analysis into the topology optimization problems. Firstly, geometrical nonlinear response analysis method of the compliant mechanisms is developed based on the Total-Lagrange finite element formulation, the incremental scheme and the Newton-Raphson iteration method. Secondly, a multi-objective topology optimal model of compliant mechanisms considering the uncertainties of the applied loads and the geometry descriptions is established. The objective function is defined by minimum the compliance and maximum the geometric advantage to meet both the stiffness and the flexibility requirements, and the reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Thirdly, the computation of the sensitivities is developed with the adjoint method and the optimization problem is solved by using the Method of Moving Asymptotes. Finally, through numerical calculations, reliability-based topology designs with geometric nonlinearity of a typical compliant micro-gripper and a multi-input and multi-output compliant sage are obtained. The importance of considering uncertainties and geometric nonlinearity is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs, which shows that the reliability-based topology optimization yields mechanisms that are more reliable than those produced by deterministic topology optimization.

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13

Matsuda, H., C. Morita, and T. Sakiyama. "Geometrical nonlinear analysis of rectangular mindlin plates." Computers & Structures 41, no. 4 (January 1991): 869–74. http://dx.doi.org/10.1016/0045-7949(91)90196-s.

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14

Rezaiee-Pajand, Mohammad, and Rahele Naserian. "Geometrical nonlinear analysis based on optimization technique." Applied Mathematical Modelling 53 (January 2018): 32–48. http://dx.doi.org/10.1016/j.apm.2017.08.003.

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15

Becker, A., V. Berkhahn, R. Kahn, and E. Stein. "Geometrical nonlinear limit load analysis plane frames." Communications in Applied Numerical Methods 3, no. 5 (September 1987): 373–80. http://dx.doi.org/10.1002/cnm.1630030505.

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16

Wood, Richard D. "Analysis of geometrically nonlinear structures." Advances in Engineering Software 28, no. 1 (January 1997): 83–84. http://dx.doi.org/10.1016/s0965-9978(96)00037-3.

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17

Yi, Zhong, and Cheng Zhi Yuan. "Mathematical Analysis on Helicoids Architectural Form." Advanced Materials Research 790 (September 2013): 273–77. http://dx.doi.org/10.4028/www.scientific.net/amr.790.273.

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In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.

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18

Zhao, Rui, Lu Sun, and Rui Li. "Analysis and Application of Deflection Curve Equation Expressed in Terms of Geometrical Parameters for Compressed Bars." Advanced Materials Research 291-294 (July 2011): 3296–99. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.3296.

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A new solution to geometrically nonlinear problems is presented. It has been found that the deflection curve equation expressed in terms of geometrical parameters for a compressed bar is a result of superposition by an Euler’s curve for two-force member in buckling equilibrium and a deformation equation for two-force member in stable equilibrium. Corresponding with the superposition of deflection curves, the load case of the compressed bar is divided into an axial force with a moment and an axial force with a shear force applied to the two-force member respectively. The analytic principle and the deflection curve equation for compressed bars can be applicable to geometrical nonlinear analysis or buckling problems, which is called analytical methods. The decision rule for the equilibrium property of the deflection curve expressions is presented. Practical applications of analytical methods show that some brief formulas can be obtained in the load case without shear forces.

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19

Mohammed Saeed, Najmadeen, and Ahmed Aulla Manguri. "An Approximate Linear Analysis of Structures Utilizing Incremental Loading of Force Method." ISSUE SIX 4, no. 6 (June 30, 2020): 37–44. http://dx.doi.org/10.25079/ukhjse.v4n1y2020.pp37-44.

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A relatively simple technique has been introduced in this paper. The approach is based on the Linear Force Method (FM) with discretion of the applied loads to the subsequence steps and updating coordinates in each iteration to have new geometrical property. The accuracy of the technique depends on the size of the discretion which depends on the number of iterations. A small change in the configuration could hugely affect the displacement and internal forces in geometrically nonlinear structures, that’s why the current approach is vital. The proposed technique is validated with other techniques of nonlinear analysis of the structures with a very good agreement in both terms of external nodal displacements and internal bar forces.

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20

Mohammed Saeed, Najmadeen, and Ahmed Aulla Manguri. "An Approximate Linear Analysis of Structures Utilizing Incremental Loading of Force Method." ISSUE SIX 4, no. 6 (June 30, 2020): 37–44. http://dx.doi.org/10.25079/ukhjse.v4n2y2020.pp37-44.

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A relatively simple technique has been introduced in this paper. The approach is based on the Linear Force Method (FM) with discretion of the applied loads to the subsequence steps and updating coordinates in each iteration to have new geometrical property. The accuracy of the technique depends on the size of the discretion which depends on the number of iterations. A small change in the configuration could hugely affect the displacement and internal forces in geometrically nonlinear structures, that’s why the current approach is vital. The proposed technique is validated with other techniques of nonlinear analysis of the structures with a very good agreement in both terms of external nodal displacements and internal bar forces.

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21

Zerkane, Ahmed, Khalid El Bikri, and Rhali Benamar. "A Homogenization Procedure for Nonlinear Free Vibration Analysis of Functionally Graded Beams Resting on Nonlinear Elastic Foundations." Applied Mechanics and Materials 232 (November 2012): 427–31. http://dx.doi.org/10.4028/www.scientific.net/amm.232.427.

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The present work deals with a homogenization procedure (HP), which is developed to reduce the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) resting on elastic nonlinear foundation with immovable ends to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results.

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22

Badiale, M. "Geometrical Properties of Fully Nonlinear Equations and an Application to Singularities." Journal of Differential Equations 112, no. 1 (August 1994): 33–52. http://dx.doi.org/10.1006/jdeq.1994.1094.

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23

Falkowicz, Katarzyna. "Numerical analysis of behaviour of compressed thin-walled Z-profiles weakened by holes." MATEC Web of Conferences 252 (2019): 07010. http://dx.doi.org/10.1051/matecconf/201925207010.

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This paper presents the results of numerical analysis conducted to investigate compressed thin-walled Z-profile weakened by holes with variable geometrical parameters. The specimens made of constructional steel were articulately supported on the edges of the cross-section in the upper and lower parts. The FEM analysis examined the nonlinear stability of these structures in the post-buckling state, where the mode of buckling was forced to ensure their stable behaviour. The numerical computations were performed within the geometrically nonlinear range until the yield point was reached. The investigation involved determining the effect of holes sizes on allowable operational loads. Numerical analysis was conducted with the Abaqus commercial FEM software package.

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Chang, T. P., and H. C. Chang. "Nonlinear vibration analysis of geometrically nonlinear shell structures." Mechanics Research Communications 27, no. 2 (March 2000): 173–80. http://dx.doi.org/10.1016/s0093-6413(00)00078-1.

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Ren, Yong Sheng, and Xiang Hong Du. "Nonlinear Model of Thin-Walled Composite Beams with Moderate Deflections." Applied Mechanics and Materials 29-32 (August 2010): 22–27. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.22.

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A geometrically nonlinear model for thin-walled, single-cell composite beams is developed by using variational formulation and the variational-asympotical method. The structural modeling is split into two parts: a two-dimensional analysis over the cross section, and a geometrically nonlinear analysis of a beam along the beam span. The nonlinear model is based on the assumption of moderate beam deflection, accounting for the pitch angle and extends the linear analysis model for anisotropic thin-walled beams. By employing the Galerkin’s method, an nonlinear algebraic equations is derived and then solved by means of an incremental Newton-Raphson method. Numerical results are obtained for one cantilevered box beam: Circumferentially Uniform Stiffness(CUS), under external load to investigate the effect of geometric nonlinearity and the effects of the fiber orientation, laminate stacking sequence, are also addressed.

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PICHAL, Radek, and Josef MACHACEK. "BUCKLING AND POST-BUCKLING OF PRESTRESSED STAINLESS STEEL STAYED COLUMNS." Engineering Structures and Technologies 9, no. 2 (June 14, 2017): 63–69. http://dx.doi.org/10.3846/2029882x.2016.1277169.

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Prestressed stayed compression members are frequently required as very slender load-bearing structural components by both investors and architects. Behavior of these members depends on their geometrical and material properties, prestressing and boundary conditions. In the paper are discussed respective critical buckling loads and post-buckling paths with regards to 2D and 3D GMNIA (geometrically and materially nonlinear analysis with imperfections) using ANSYS software. Former tests and recent detailed analyses of other authors are commented with respect to the 3D analysis, level of imperfections, boundary conditions at central crossarm (fixed or sliding stays) and nonlinear stainless steel material.

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27

Thi Phuong, Nguyen, Vu Hoai Nam, and Dang Thuy Dong. "Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment." Journal of Sandwich Structures & Materials 22, no. 4 (June 12, 2018): 1157–83. http://dx.doi.org/10.1177/1099636218782645.

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A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.

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28

Luo, Albert C. J. "A geometrically-nonlinear plate theory." Communications in Nonlinear Science and Numerical Simulation 4, no. 2 (June 1999): 136–40. http://dx.doi.org/10.1016/s1007-5704(99)90027-8.

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29

DEGEE, HERVE, BARBARA ROSSI, and DENIS JEHIN. "GEOMETRICALLY NONLINEAR ANALYSIS OF STEEL STORAGE RACKS SUBMITTED TO EARTHQUAKE LOADING." International Journal of Structural Stability and Dynamics 11, no. 05 (October 2011): 949–67. http://dx.doi.org/10.1142/s0219455411004415.

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Steel storage racks are light and flexible structures. When submitted to earthquake loading, they can exhibit very large transverse displacements and are thus prone to significant consequences of second-order geometrical effects. In the context of the drafting of European recommendations for the design of steel pallet racks for their seismic resistance, this paper presents a parameter study comparing the various methods commonly used in practice for analyzing the seismic structural behavior of racks (i.e. "modal response spectrum analysis" and "lateral force method analysis") as well as the different ways to account for geometrically nonlinear effects in these conventional methods of analysis in the case of structures designed for low ductility.

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30

Yeh, Wen-Cheng. "A Co-Rotational Meshfree Method for the Geometrically Nonlinear Analysis of Structures." Applied Sciences 11, no. 14 (July 20, 2021): 6647. http://dx.doi.org/10.3390/app11146647.

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This paper presents a co-rotational beam formulation, which is used for geometric nonlinear analysis with the differential reproducing kernel (DRK) approximation collocation method. The present formulation, based on the Timoshenko beam hypothesis, is capable of effectively solving geometrically nonlinear problems such as large deformation, postbuckling, lateral buckling, and snap-through problems. The kinematics have been constructed with the concept of co-rotational formulation adopted in the finite element method (FEM). A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method, combined with the Newton–Raphson method, is employed to solve the strong forms of the geometrically nonlinear problems. The DRK method takes full advantage of the meshfree method. Moreover, only a scattered set of nodal points is necessary for the discretization. No elements or mesh connectivity data are required. Therefore, DRK will be able to completely circumvent the problems of mesh dependence and mesh distortion. The effectiveness of this study and its performance are shown through several numerical applications.

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31

Harko, Tiberiu, Chor Yin Ho, Chun Sing Leung, and Stan Yip. "Jacobi stability analysis of the Lorenz system." International Journal of Geometric Methods in Modern Physics 12, no. 07 (July 10, 2015): 1550081. http://dx.doi.org/10.1142/s0219887815500814.

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We perform the study of the stability of the Lorenz system by using the Jacobi stability analysis, or the Kosambi–Cartan–Chern (KCC) theory. The Lorenz model plays an important role for understanding hydrodynamic instabilities and the nature of the turbulence, also representing a nontrivial testing object for studying nonlinear effects. The KCC theory represents a powerful mathematical method for the analysis of dynamical systems. In this approach, we describe the evolution of the Lorenz system in geometric terms, by considering it as a geodesic in a Finsler space. By associating a nonlinear connection and a Berwald type connection, five geometrical invariants are obtained, with the second invariant giving the Jacobi stability of the system. The Jacobi (in)stability is a natural generalization of the (in)stability of the geodesic flow on a differentiable manifold endowed with a metric (Riemannian or Finslerian) to the non-metric setting. In order to apply the KCC theory, we reformulate the Lorenz system as a set of two second-order nonlinear differential equations. The geometric invariants associated to this system (nonlinear and Berwald connections), and the deviation curvature tensor, as well as its eigenvalues, are explicitly obtained. The Jacobi stability of the equilibrium points of the Lorenz system is studied, and the condition of the stability of the equilibrium points is obtained. Finally, we consider the time evolution of the components of the deviation vector near the equilibrium points.

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32

Karabutov, N. N. "S-synchronization Structural Identiﬁability and Identiﬁcation of Nonlinear Dynamic Systems". Mekhatronika, Avtomatizatsiya, Upravlenie 21, № 6 (4 червня 2020): 323–36. http://dx.doi.org/10.17587/mau.21.323-336.

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An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

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33

Luo, Xu, Xin Sha Fu, Li Xiong Gu, and Lu Rong Cai. "Nonlinear Stability Analysis of Long-Span Suspension Bridge Cable Tower." Advanced Materials Research 1030-1032 (September 2014): 802–6. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.802.

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The cable tower is the bearing component of long-span suspension bridges, and its structure is very high and bear large force, which determines the stability and is the key of safety control. As for the height of the main tower of a long-span suspension bridge up to 195.3 m, the finite element software ANSYS is used to establish a three-dimensional finite element model (FEM), and the effects of geometric nonlinearity and material nonlinearity on the stability of the main tower are analyzed. The calculation results show that geometrical nonlinearity and material defects have significant influence on the main tower stability, and the nonlinear stability should be considered under wind load in the design calculation.

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34

da Silva, João Vitor. "GeometricC1+αregularity estimates for nonlinear evolution models". Nonlinear Analysis 184 (липень 2019): 95–115. http://dx.doi.org/10.1016/j.na.2019.01.031.

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35

MORITA, Chihiro, Hiroshi MATSUDA, and Takeshi SAKIYAMA. "ANALYSIS ON GEOMETRICAL NONLINEAR BEHAVIOR OF RECTANGULAR PLATES." Doboku Gakkai Ronbunshu, no. 455 (1992): 35–43. http://dx.doi.org/10.2208/jscej.1992.455_35.

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36

Rezaiee-Pajand, Mohammad, Rahele Naserian, and Hossein Afsharimoghadam. "Geometrical nonlinear analysis of structures using residual variables." Mechanics Based Design of Structures and Machines 47, no. 2 (January 20, 2019): 215–33. http://dx.doi.org/10.1080/15397734.2018.1545585.

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37

He, Yuanping, and T. Bryant Moodi. "Geometrical optics and post shock behavior for nonlinear conservation laws." Applicable Analysis 57, no. 1-2 (June 1995): 145–76. http://dx.doi.org/10.1080/00036819508840344.

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38

Bakr, E. M., and A. A. Shabana. "Geometrically nonlinear analysis of multibody systems." Computers & Structures 23, no. 6 (January 1986): 739–51. http://dx.doi.org/10.1016/0045-7949(86)90242-7.

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39

Allen, H. G., and H. H. Al-Qarra. "Geometrically nonlinear analysis of structural membranes." Computers & Structures 25, no. 6 (January 1987): 871–76. http://dx.doi.org/10.1016/0045-7949(87)90201-x.

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40

Xia, J. M., D. M. Wei, and R. H. Jin. "Meshless analysis of geometrically nonlinear beams." Journal of Physics: Conference Series 96 (February 1, 2008): 012005. http://dx.doi.org/10.1088/1742-6596/96/1/012005.

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41

Moita, José S., Aurélio L. Araújo, Cristóvão M. Mota Soares, Carlos A. Mota Soares, and José Herskovits. "Geometrically nonlinear analysis of sandwich structures." Composite Structures 156 (November 2016): 135–44. http://dx.doi.org/10.1016/j.compstruct.2016.01.018.

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42

Li, Q. S., and J. M. Chen. "Nonlinear Analysis of Single-Layer Reticulated Spherical Shells Under Static and Dynamic Loads." Journal of Vibration and Control 10, no. 5 (May 2004): 731–54. http://dx.doi.org/10.1177/1077546304040236.

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A nonlinear finite element technique is developed for analyzing the nonlinear static and dynamic responses as well as the nonlinear stability of single-layer reticulated shells under external loads, in which the nonlinear three-dimensional beam elements are employed. Using the updated Lagrangian formulation, we derive a tangent stiffness matrix of three-dimensional beam element, considering the geometric nonlinearity of the element. Moreover, the modified Newton-Raphson method is employed for the solution of the nonlinear equilibrium equations, and the Newmark-β method is adopted for determining the seismic response of single-layer reticulated shells. An improved arc-length method, in which the current stiffness parameter is used to reflect the nonlinear degree of such space structures, is presented for determining the load increment for the structural stability analysis. In addition, an accurate incremental method is developed for computing the large rotations of the space structures. The developed approach is presented in matrix form, which is particularly convenient for developing a computer program. Numerical examples are presented to illustrate the application of the present method and to investigate the effects of the geometrical nonlinearity of the space structures.

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43

YU. VETYUKOV. "CONSISTENT APPROXIMATION FOR THE STRAIN ENERGY OF A 3D ELASTIC BODY ADEQUATE FOR THE STRESS STIFFENING EFFECT." International Journal of Structural Stability and Dynamics 04, no. 02 (June 2004): 279–92. http://dx.doi.org/10.1142/s0219455404001239.

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Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

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44

Tanriöver, H., and E. Şenoca. "Nonlinear transient analysis of moderately thick rectangular composite plates." Aeronautical Journal 114, no. 1157 (July 2010): 437–44. http://dx.doi.org/10.1017/s0001924000003912.

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Abstract This paper presents an analytical-numerical methodology for the geometrically nonlinear analysis of laminated composite plates under dynamic loading. The methodology employs Galerkin technique, in which suitable polynomials are chosen as trial functions. In the solution process, Newmark’s scheme for time integration, and modified Newton-Raphson method for the solution of resulting nonlinear equations are used. In the formulation, first order shear deformation theory based on Mindlin’s hypothesis and von Kármán type geometric nonlinearity are considered. The results are compared to that of finite strips, and Chebyshev series published elsewhere. The method is found to determine closely both the displacements and the stresses. A finite element analysis has also been carried out for the validation of the results. The present method can be efficiently and easily applied for the nonlinear transient analysis of laminated composite plates with various boundary conditions.

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45

Hanaor, Ariel. "Aspects of Design of Double-Layer Tensegrity Domes." International Journal of Space Structures 7, no. 2 (June 1992): 101–13. http://dx.doi.org/10.1177/026635119200700204.

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Double-layer tensegrity domes are formed from double-layer tensegrity grids (DLTGs) with cured surfaces. Typically such domes consist of truncated pyramidal units or their derivatives joined together. Unlike flat DLTGs, the geometric configuration of the dome involves shape finding. The initial, prestressed geometry depends on the constraints governing the construction of the dome. Both shape finding and load analysis involve geometric non-linearities, but the extent of nonlinear behaviour under load, i.e. the magnitude of deflections, depends on a number of factors. While tensegrity structures, like other prestressed cable networks, are often geometrically flexible, geometrically rigid configurations, involving only elastic deformations, are feasible.

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46

Pavelko, Vitalijs. "Application of the Nonlinear Model of a Beam for Investigation of Interlaminar Fracture Toughness of Layered Composite." Key Engineering Materials 665 (September 2015): 273–76. http://dx.doi.org/10.4028/www.scientific.net/kem.665.273.

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Earlier presented the geometrically nonlinear model of a flexible beam (cylindrical bending of a plate) was used for analysis of post-buckling behavior of the layered composite with delamination at compression. In this paper the model is used for more details nonlinear analysis of double cantilever beam (DCB) that used in standard test for determination of the interlaminar fracture toughness composites with delamination-type damage. The main advantage of the model is a precise description of the curved axis of the beam (plate) without linearization or other higher order approximations. The exact solution of bending differential equation finally can be expressed in terms of the incomplete elliptic integrals of the first and second kind. The model describes only geometrically nonlinear effect of DCB arms bending (global effect) and should be combined with the procedure of effective delamination extension to correct DCB arms rotation at delamination front (local effect). First of all the nonlinear model can serve as a tool to estimate the possible error due the geometrical nonlinearity in comparison with linear solution. On the other hand, this model can be effectively used to determine interlaminar fracture toughness using DCB samples at large deflections. Validation of the model is made using data of standard tests of glass/epoxy DCB samples.

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47

Noh, Sam Young, and Sang Yun Lee. "Structural Behaviour Evaluation of Natural Draught Cooling Towers under the Consideration of Shell-Geometric Parameters." Applied Mechanics and Materials 284-287 (January 2013): 1396–400. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.1396.

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In the design procedure of the cooling tower the form-finding of the shell is the most important process, because the shape of the shell determines the sensitivity of dynamic behavior of the whole tower against wind excitation. The purpose of the study is the investigation of the influences of the geometric parameters of the cooling tower shell on the structural behavior. The geometric parameters - height of throat, angle of base lintel and radius of top lintel - were analyzed in detail. In the linear analysis the influence of each geometrical parameter will be evaluated by the required amount of the reinforcement steel. The realistic behaviours of the towers with various geometries, found out by geometrically and physically non-linear analysis, will be discussed in detail. Each geometry parameter influence will be evaluated by the comparison of the damage index developments in the tower under increasing wind effect. Herein a damage indicator is defined by means of the modal parameters; natural frequencies and mode shapes varying according to the damage state. As a result, a hyperbolic rotational shell with the small radius overall will yield the shell geometry with a higher first natural frequency and thus a wind-insensitive structure. Linearly and nonlinearly numerical simulations demonstrate influence of the shell-geometric parameters on structural behaviours. The results of this study may be informative for the form-finding of the cooling tower shell.

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48

Manteuffel, T. A., S. F. McCormick, J. G. Schmidt, and C. R. Westphal. "First‐Order System Least Squares for Geometrically Nonlinear Elasticity." SIAM Journal on Numerical Analysis 44, no. 5 (January 2006): 2057–81. http://dx.doi.org/10.1137/050628027.

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49

Yangui, M., S. Bouaziz, M. Taktak, M. Haddar, and A. El-Sabbagh. "Nonlinear Analysis of Twisted Wind Turbine Blade." Journal of Mechanics 34, no. 3 (December 12, 2016): 269–78. http://dx.doi.org/10.1017/jmech.2016.120.

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AbstractModal analysis is developed in this paper in order to study the dynamic characteristics of rotating segmented blades assembled with spar. Accordingly, a three dimensional finite element model was built using the three node triangular shell element DKT18, which has six degrees of freedom, to model the blade and the spar structures. This study covers the effect of rotation speed and geometrically nonlinear problems on the vibration characteristics of rotating blade with various pretwist angles. Likewise, the effect of the spar in the blade is taken into consideration. The equation of motion for the finite element model is derived by using Hamilton's principle, while the resulting nonlinear equilibrium equation is solved by applying the Newmark method combined with the Newton Raphson schema. Results show that the natural frequencies increase by taking account of the spar, they are also proportional to the angular rotation speed and influenced by geometric nonlinearity and pretwist angle.

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50

Bahari, A. R., M. A. Yunus, M. N. Abdul Rani, M. A. Ayub, and A. Nalisa. "Numerical And Experimental Investigations of Nonlinearity Behaviour In A Slender Cantilever Beam." MATEC Web of Conferences 217 (2018): 02008. http://dx.doi.org/10.1051/matecconf/201821702008.

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Nonlinear problem is always occur in slender structures that are usually characterized by large displacements and rotations but small strains. Linear design assumption could lead to premature failure if the structure behaves nonlinearly. In this paper, the static displacement of a slender beam subjected to point load is investigated numerically by incorporating the large amplitude of the displacement. Two types of numerical analyses are performed at a full-scale finite element model which is linear static and geometric nonlinear implicit static. the results of the FEA linear static analysis are compared with the results from the FEA geometric nonlinear implicit static analysis. It shows that very high different load-displacement value response. Experimental static displacement test has been performed to validate both numerical results.

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