• Structural Engineering and Mechanics
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• 제11권5호
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• pp.519-534
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• 2001

The effect of the initial imperfections on the nonlinear behaviors and ultimate strength of the thin-walled members subjected to the axial loads, obtained by the finite element stability analysis, are examined. As the initial imperfections, the bucking mode shapes of the members are adopted. The buckling mode shapes of the thin-walled members are obtained by the transfer matrix method. In the finite element stability analysis, isoparametric degenerated shell element is used, and the geometrical and material nonlinearity are considered based on the Green Lagrange strain definition and the Prandtl-Reuss stress-strain relation following the von Mises yield criterion. The U-, box- and I-section members subjected to the axial loads are adopted for numerical examples, and the effects of the initial imperfections on the nonlinear behaviors and ultimate strength of the members are examined.

• Structural Engineering and Mechanics
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• 제22권2호
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• pp.223-240
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• 2006

Taking into account the geometrical and material nonlinearities, an ultimate behavior of reinforced concrete cooling tower shell in hyperbolic configuration is presented. The design wind pressures suggested in the guidelines of the US (ACI) and Germany (VGB), with or without the effect of internal suction, are employed in the analysis to examine the qualitative and quantitative characteristics of each design wind pressure. The geometrical nonlinearity is incorporated by the Green-Lagrange strain tensor. The nonlinear features of concrete, such as the nonlinear stress-strain relation in compression, the tensile cracking with the smeared crack model, an effect of tension stiffening, are taken into account. The biaxial stress state in concrete is represented by an improved work-hardening plasticity model. From the perspective of quality of wind pressures, the two guidelines are determined as highly correlated each other. Through the extensive analysis on the Niederaussem cooling tower in Germany, not only the ultimate load is determined but also the mechanism of failure, distribution of cracks, damage processes, stress redistributions, and mean crack width are examined.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.335-342
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• 2002

A continuum-based design sensitivity analysis (DSA) method fur non-shape problems is developed for geometrically nonlinear elastic structures. The non-shape problem is characterized by the design variables that are not associated with the domain of system like sizing, material property, loading, and so on. Total Lagrangian formulation with the Green-Lagrange strain and the second Piola-Kirchhoff stress is employed to describe the geometrically nonlinear structures. The spatial domain is discretized using the 4-node isoparametric plane stress/strain elements. The resulting nonlinear system is solved using the Newton-Raphson iterative method. To take advantage of the derived analytical sensitivity In topology optimization, a fast and efficient design sensitivity analysis method, adjoint variable method, is employed and the material property of each element is selected as non-shape design variable. Combining the design sensitivity analysis method and a gradient-based design optimization algorithm, an automated design optimization method is developed. The comparison of the analytical sensitivity with the finite difference results shows excellent agreement. Also application to the topology design optimization problem suggests a very good insight for the layout design.

• Steel and Composite Structures
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• 제34권2호
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• pp.279-288
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• 2020

The computational post-buckling strength of the tilted sandwich composite shell structure is evaluated in this article. The computational responses are obtained using a mathematical model derived using the higher-order type of polynomial kinematic in association with the through-thickness stretching effect. Also, the sandwich deformation behaviour of the flexible soft-core sandwich structural model is expressed mathematically with the help of a generic nonlinear strain theory i.e. Green-Lagrange type strain-displacement relations. Subsequently, the model includes all of the nonlinear strain terms to account the actual deformation and discretized via displacement type of finite element. Further, the computer code is prepared (MATLAB environment) using the derived higher-order formulation in association with the direct iterative technique for the computation of temperature carrying capacity of the soft-core sandwich within the post-buckled regime. Further, the nonlinear finite element model has been tested to show its accuracy by solving a few numerical experimentations as same as the published example including the consistency behaviour. Lastly, the derived model is utilized to find the temperature load-carrying capacity under the influences of variable factors affecting the soft-core type sandwich structural design in the small (finite) strain and large deformation regime including the effect of tilt angle.

• 대한조선학회논문집
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• 제44권2호
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• pp.130-138
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• 2007

A coupled variational equation for fluid-structure interaction (FSI) problems is derived from a steady state Navier-Stokes equation for incompressible Newtonian fluid and an equilibrium equation for geometrically nonlinear structures. For a fully coupled FSI formulation, between fluid and structures, a traction continuity condition is considered at interfaces where a no-slip condition is imposed. Under total Lagrange formulation in the structural domain, finite rotations are well described by using the second Piola-Kirchhoff stress and Green-Lagrange strain tensors. An adjoint shape design sensitivity analysis (DSA) method based on material derivative approach is applied to the FSI problem to develop a shape design optimization method. Demonstrating some numerical examples, the accuracy and efficiency of the developed DSA method is verified in comparison with finite difference sensitivity. Also, for the FSI problems, a shape design optimization is performed to obtain a maximal stiffness structure satisfying an allowable volume constraint.

• Structural Engineering and Mechanics
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• 제40권2호
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Advances in materials Research
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• 제5권4호
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• pp.205-221
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• 2016

In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt's micromechanical model through the power-law distribution with and without temperature dependent properties. The mathematical model is developed using the higher-order shear deformation theory in conjunction with Green-Lagrange type nonlinear strain to consider large geometrical distortion under thermal load. The efficacy of the proposed model has been checked and the effects of various geometrical and material parameters on the buckling load are analysed in details.

• Advances in nano research
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• 제7권3호
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• pp.181-190
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• 2019

The thermal buckling temperature values of the graded carbon nanotube reinforced composite shell structure is explored using higher-order mid-plane kinematics and multiscale constituent modeling under two different thermal fields. The critical values of buckling temperature including the effect of in-plane thermal loading are computed numerically by minimizing the final energy expression through a linear isoparametric finite element technique. The governing equation of the multiscale nanocomposite is derived via the variational principle including the geometrical distortion through Green-Lagrange strain. Additionally, the model includes different grading patterns of nanotube through the panel thickness to improve the structural strength. The reliability and accuracy of the developed finite element model are varified by comparison and convergence studies. Finally, the applicability of present developed model was highlight by enlighten several numerical examples for various type shell geometries and design parameters.

• 한국자동차공학회논문집
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• 제14권6호
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• pp.17-23
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• 2006

Rubber materials have the nonlinear, large deformation and viscoelastic behavior. W.D. Kim et al. studied these characteristics through the static, fatigue, dynamic, aging and viscoelastic test. This paper discussed that the properties of engine mounting rubber, such as static stiffness, fatigue life and damping factor, are predicted based on CAE by using material properties acquired by the report of Kim et al. In result, the static stiffness of engine mounting rubber is predicted approximately in comparison with test value. Also, it was confirmed that the relationship of fatigue life and Green-Lagrange strain in specimen was the valid tool to predict the fatigue life of engine mounting rubber. From the results of transient viscoelastic analysis the damping factor changed rapidly at the range less than 8hz.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.565-578
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• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.