• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly 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. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.337-346
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• 2018

The purpose of this study is to investigate thermal post-buckling analysis of a laminated composite beam subjected under uniform temperature rising with temperature dependent physical properties. The beam is pinned at both ends and immovable ends. Under temperature rising, thermal buckling and post-buckling phenomena occurs with immovable ends of the beam. In the nonlinear kinematic model of the post-buckling problem, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. Also, material properties of the laminated composite beam are temperature dependent: that is the coefficients of the governing equations are not constant. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The effects of the fibber orientation angles, the stacking sequence of laminates and temperature rising on the post-buckling deflections, configurations and critical buckling temperatures of the composite laminated beam are illustrated and discussed in the numerical results. Also, the differences between temperature dependent and independent physical properties are investigated for post-buckling responses of laminated composite beams.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.109-125
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• 2012

Post-buckling behavior of Timoshenko beams subjected to uniform temperature rising with temperature dependent physical properties are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly 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. The beams considered in numerical examples are made of Austenitic Stainless Steel (316). The convergence studies are made. In this study, the difference between temperature dependent and independent physical properties are investigated in detail in post-buckling case. The relationships between deflections, thermal post-buckling configuration, critical buckling temperature, maximum stresses of the beams and temperature rising are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.15 no.5
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly 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. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1931-1942
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• 1997

A new load/displacement parameter method is developed for the cases that loads are applied to one or more points, and displacements of a structure are controlled at one or more points sinultaneously. The procedure exploits a generalized Riks method, which utilizes load/displacement parameters as scaling factors in order to analyze the post-buckling phenomena including snap-through or snap-back. A convergence characteristic is improved by employing new relaxation factors in incremental displacement parameter, particularly at the region where exhibits severe numerical instability. The improved performance is illustrated by means of numerical example.

• Structural Engineering and Mechanics
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• v.19 no.2
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• pp.153-172
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• 2005

A new load/displacement parameter method is proposed for the simultaneous control of applied loads and structural displacements at one or more points. The procedure is based on a generalized Riks' method, which utilizes load/displacement parameters as scaling factors to analyze post-buckling phenomena including snap-through or snap-back. The convergence characteristics are improved by employing new relaxation factors through an incremental displacement parameter, particularly in a region that exhibits severe numerical instability. The improved performance is illustrated by means of a numerical example.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1237-1258
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• 2015

This paper proposes a simple inelastic analysis approach to efficiently map out the complete nonlinear post-collapse (strain-softening) response and the maximum load capacity of axially loaded concrete encased steel composite columns (stub and slender). The scheme simultaneously incorporates the influences of difficult instabilizing phenomena such as concrete confinement, initial geometric imperfection, geometric nonlinearity, buckling of reinforcement bars and local buckling of structural steel, on the overall behavior of the composite columns. The proposed numerical method adopts fiber element discretization and an iterative M${\ddot{u}}$ller's algorithm with an additional adaptive technique that robustly yields solution convergence. The accuracy of the proposed analysis scheme is validated through comparisons with various available experimental benchmarks. Finally, a parametric study of various key parameters on the overall behaviors of the composite columns is conducted.

• Advances in nano research
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• v.16 no.6
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• pp.623-638
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• 2024

This study investigates the thermal post-buckling behavior of concrete eccentric annular sector plates reinforced with graphene oxide powders (GOPs). Employing the minimum total potential energy principle, the plates' stability and response under thermal loads are analyzed. The Haber-Schaim foundation model is utilized to account for the support conditions, while the transform differential quadrature method (TDQM) is applied to solve the governing differential equations efficiently. The integration of GOPs significantly enhances the mechanical properties and stability of the plates, making them suitable for advanced engineering applications. Numerical results demonstrate the critical thermal loads and post-buckling paths, providing valuable insights into the design and optimization of such reinforced structures. This study presents a machine learning algorithm designed to predict complex engineering phenomena using datasets derived from presented mathematical modeling. By leveraging advanced data analytics and machine learning techniques, the algorithm effectively captures and learns intricate patterns from the mathematical models, providing accurate and efficient predictions. The methodology involves generating comprehensive datasets from mathematical simulations, which are then used to train the machine learning model. The trained model is capable of predicting various engineering outcomes, such as stress, strain, and thermal responses, with high precision. This approach significantly reduces the computational time and resources required for traditional simulations, enabling rapid and reliable analysis. This comprehensive approach offers a robust framework for predicting the thermal post-buckling behavior of reinforced concrete plates, contributing to the development of resilient and efficient structural components in civil engineering.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.17-27
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• 1995

For the post-buckling and elasto-plastic analysis of shell structures, the total Lagrangian formulation is presented based upon the degenerated shell element. Geometrically correct formulation is developed by updating the direction of normal vectors in the iteration process and evaluating the total Green-Lagrange stain corresponding U total displacements. In the calculation of the stiffness matrix, the element formulation takes into account the effect of finite rotation increments by retaining second order rotation terms in the incremental displacement field. The selective or reduced integration scheme using the heterosis element is applied in order to overcome both shear locking phenomena and the zero energy mode. The load/displacement incremental scheme is adopted for geometric non-linear F .E. analysis. Based on such methodology, the computer program is developed and numerical examples to demonstrate the accuracy and the effectiveness of the proposed shell element are presented and compared with references's results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.503-512
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• 1990

In this study, a penalty method effective for the case that has no snap-back phenomenon, is proposed and an adaptive method which choose the penalty method or Riks' type method, is suggested for the case of snap-back problem. And for the case that loads are applied to one or more points of a structure, the Riks' method is applied in general, but under certain condition choice of new incremental load parameter is suggested to accelerate the convergence rate. Finally, for the case that displacements of a structure are controlled at one or more points Riks' type method is proposed. In this case, the proposed method is applied in general but under certain condition it is recommended to choose other incremental displacement parameter to eliminate probable divergence. Five examples are analysed and compared with the result of published literature.