• Structural Engineering and Mechanics
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• v.47 no.1
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• pp.27-44
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• 2013

A finite element computational procedure for the accurate analysis of quasistatic thermorheological complex structures response is developed. The geometrical nonlinearity, arising from large displacements and rotations (but small strains), is accounted for by the total Lagrangian description of motion. The Schapery's nonlinear single-integral viscoelastic constitutive model is modified for a time-stress-temperature-dependent behavior. The nonlinear thermo-viscoelastic constitutive equations are incrementalized leading to a recursive relationship and thereby the resulting finite element equations necessitate data storage from the previous time step only, and not the entire deformation history. The Newton-Raphson iterative scheme is employed to obtain a converged solution for the non-linear finite element equations. The developed numerical model is verified with the previously published works and a good agreement with them is found. The applicability of the developed model is demonstrated by analyzing two examples with different thermal/mechanical loading histories.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.263-276
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• 2007

This paper presents a fuzzy finite element model for the analysis of structures in the presence of multiple uncertainties. A new methodology to evaluate the cumulative effect of multiple uncertainties on structural response is developed in the present work. This is done by modifying Muhanna's approach for handling single uncertainty. Uncertainty in load and material properties is defined by triangular membership functions with equal spread about the crisp value. Structural response is obtained in terms of fuzzy interval displacements and rotations. The results are further post-processed to obtain interval values of bending moment, shear force and axial forces. Membership functions are constructed to depict the uncertainty in structural response. Sensitivity analysis is performed to evaluate the relative sensitivity of displacements and forces to uncertainty in structural parameters. The present work demonstrates the effectiveness of fuzzy finite element model in establishing sharp bounds to the uncertain structural response in the presence of multiple uncertainties.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.277-298
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• 2002

In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried out by mixed finite element method based on the G$\hat{a}$teaux differential. New boundary conditions are established for plates on Pasternak foundation. This method is developed and applied to numerous problems by Ak$\ddot{o}$z and his co-workers. In dynamic analysis, the problem reduces to the solution of a standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns. The element performance is assessed by comparison with numerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamic analysis. Shear locking effects are tested as far as $h/2a=10^{-6}$ and it is observed that REC32 is free from shear locking.

• Computational Structural Engineering
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• v.8 no.2
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• pp.133-140
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• 1995

The buckling analysis of Glass Fiber Reinforced Plastic pipes was studied through a three dimentsional finite element method. In the finite element analysis, an improved degenerated shell element with incompatible modes and assumed shear strain fields are employed with 3 displacements and 2 rotations for each joints. Buckling analysis is carried out for various thicknesses and different fiber orientations. Finite element results show that the buckling load increases as the thickness does with the variation of coupling stiffness.

• Steel and Composite Structures
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• v.26 no.6
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• pp.733-743
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• 2018

This paper presents post-buckling responses of a simply supported laminated composite beam subjected to a non-follower axially compression loads. In the nonlinear kinematic model of the laminated beam, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The distinctive feature of this study is post-buckling analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. The effects of the fibber orientation angles and the stacking sequence of laminates on the post-buckling deflections, configurations and stresses of the composite laminated beam are illustrated and discussed in the numerical results. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the laminated composite beams.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.767-802
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• 2011

Developers of new finite elements or nonlinear solution techniques rely on discriminative benchmark tests drawn from the literature to assess the advantages and drawbacks of new formulations. Buckling benchmark tests provide a rigorous evaluation of finite elements applied to thin structures, and a complete and detailed set of reference results would therefore prove very useful in carrying out such evaluations. Results are usually presented in the form of load-deflection curves that developers must reconstruct by extracting the points, a procedure which is often tedious and inaccurate. Moreover the curves are usually given without accompanying information such as the calculation time or number of iterations it took for the model to converge, even though this type of data is equally important in practice. This paper presents ten different limit-point buckling benchmark tests, and provides for each one the reference load-deflection curve, all the points necessary to recreate the curve in tabulated form, analysis data such as calculation time, number of iterations and increments, and all of the inputs used to obtain these results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.449-456
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• 1998

A consistent finite element formation and analytic solutions are presented for spatial stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result the energy functional corresponding to the semitangential rotation is obtained, in which the elastic strain energy terms are considered restrained warping effects. We have obtained analytic solution for the lateral buckling of monosymmetric thin-walled curved beam subjected to pure bending or uniform compression and it's boundary conditions are simply supported. For finite element analysis, the two node cubic Hermitian polynomials are utilized as shape Auctions. In order to illustrate the accuracy of this study, parameter studies for lateral buckling problems of circular arch are presented and compared with available solutions and numerical results analyzed by the FEM using straight beam element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.465-472
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• 1998

In this study, analytic solution and finite element formulation for the free vibration analysis of thin-walled circular arch, based on linearized virtual work and Vlasov's assumption, including restrained warping effect and second order terms of finite semitangential rotations, is presented. The total potential energy is derived by applying the Hellinger-Reissner principle. In this formulation, all displacement parameters of deformation are defined at the centroid axis. For the finite element formulation, the two node cubic Hermitian polynomials are utilized as shape functions. In special case, potential energy functional of thin-walled curved beam with monosymmetric cross section is derived. From this methodology, analytic solution for the free vibration of monosymmetric circular arch with simply supported is derived. In order to illustrate the accuracy of this study, various parameter studies for free vibration of circular arches are presented and compared with numerical solution analyzed by the FEM using straight beam element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.239-246
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• 1997

The general formulation of free vibration and stability analysis of unsymmetric thin-walled space frames and beam-columns is presented. The kinetic and total potential energy is derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.27-36
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• 2018

The objective of this work is to analyze geometrically nonlinear static analysis a simply supported laminated composite beam subjected to a non-follower transversal point load at the midpoint of the beam. In the nonlinear model of the laminated beam, total Lagrangian finite element model of is used in conjunction with the Timoshenko beam theory. The considered non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. In the numerical results, the effects of the fiber orientation angles and the stacking sequence of laminates on the nonlinear deflections and stresses of the composite laminated beam are examined and discussed. Convergence study is performed. Also, the difference between the geometrically linear and nonlinear analysis of laminated beam is investigated in detail.