• 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.

• Structural Engineering and Mechanics
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• v.49 no.6
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• pp.727-743
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• 2014

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

• Wind and Structures
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• v.27 no.1
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• pp.59-70
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• 2018

In this paper, geometrically non-linear analysis of a functionally graded simple supported beam is investigated with porosity effect. The material properties of the beam are assumed to vary though height direction according to a prescribed power-law distributions with different porosity models. In the nonlinear kinematic model of the beam, the total Lagrangian approach is used within Timoshenko beam theory. In the solution of the nonlinear problem, the finite element method is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution such as power-law exponents, porosity coefficients, nonlinear effects on the static behavior of functionally graded beams are examined and discussed with porosity effects. The difference between the geometrically linear and nonlinear analysis of functionally graded porous beam is investigated in detail. Also, the effects of the different porosity models on the functionally graded beams are investigated both linear and nonlinear cases.

• Steel and Composite Structures
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• v.30 no.4
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• pp.327-336
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• 2019

This paper presents geometrically nonlinear behavior of cracked fiber reinforced composite beams by using finite element method with and the first shear beam theory. Total Lagrangian approach is used in the nonlinear kinematic relations. The crack model is considered as the rotational spring which separate into two parts of beams. In the nonlinear solution, the Newton-Raphson is used with incremental displacement. The effects of fibre orientation angles, the volume fraction, the crack depth and locations of the cracks on the geometrically nonlinear deflections of fiber reinforced composite are examined and discussed in numerical results. Also, the difference between geometrically linear and nonlinear solutions for the cracked fiber reinforced composite beams.

• Advances in nano research
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• v.13 no.2
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• pp.113-120
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• 2022

In this paper, a finite element (FE) simulation has been developed in order to examine the nonlinear stability of reinforced sandwich beams with graphene oxide powders (GOPs). In this regard, the nonlinear stability curves have been obtained asuming that the beam is under compressive loads leading to its buckling. The beam is considered to be a three-layered sandwich beam with metal core and GOP reinforced face sheets and it is rested on elastic substrate. Moreover, a higher-order refined beam theory has been considered to formulate the sandwich beam by employing the geometrically perfect and imperfect beam configurations. In the solving procedure, the utalized finite element simulation contains a novel beam element in which shear deformation has been included. The calculated stability curves of GOP-reinforced sandwich beams are shown to be dependent on different parameters such as GOP amount, face sheet thickness, geometrical imperfection and also center deflection.

• Journal of Fisheries and Marine Sciences Education
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• v.24 no.5
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• pp.699-711
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• 2012

An undergraduate course named computational structural analysis becomes more significant in recent years because of its important role in industries and the recent innovation in computer technology. Typically, the course consists of introduction to finite element method, utilization of general purpose finite element software, and examples focusing on static and linear analyses on various structural members such as a beam, truss, frame, arch, and cable. However, in addition to the static and linear analyses, current industries ask graduates to acquire basic knowledge on structural dynamics and nonlinear analysis, which are not listed in the conventional syllabus of the computational structural analysis. Therefore, this study develops geometrically nonlinear examples, which can help students to easily capture the fundamental nonlinear theory, software manipulation, and problem solving skills. For the purpose, five different examples are found, developed for the analyses of cables and cable nets, which naturally have strong geometrical non-linearity. In the paper, these examples are presented, discussed, and finally compared for a better subject development.

• Structural Engineering and Mechanics
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• v.40 no.2
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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.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.433-441
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• 2019

In this paper, geometrically nonlinear static analysis of laminated composite beams is investigated under hygrothermal effect. In the solution of problem, the finite element method is used within the first shear beam theory. Total Lagrangian approach is used nonlinear kinematic model. The geometrically nonlinear formulations are developed for the laminated beams with hygro-thermal effects. In the nonlinear solution of the problem, the Newton-Raphson method is used with incremental displacement. In order to verify of obtained formulations, a comparison study is performed. The effects of the fiber orientation angles, the stacking sequence of laminates, temperature rising and moisture changes on the nonlinear static displacements and configurations of the composite laminated beam are investigated in the numerical results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.3
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• pp.1-10
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• 1988

A higher order plate bending finite element using cubic in-plane displacement profiles is proposed for geometrically nonlinear analysis of thin and thick plates. The higher order plate bending element has been derived from the three dimensional plate-like continuum by discretization of the equations of motion by Galerkin weighted residual method, together with enforcing higher order plate assumptions. Total Lagrangian formulation has been used for geometrically nonlinear analysis of plates and consistent linearization by Newton-Raphson method has been performed to solve the nonlinear equations. The element characteristics have been computed by, selective reduced integration technique using Gauss quadrature to avoid shear locking phenomenon in case of extremely thin plates. Several numerical examples were solved with FEAP macro program to demonstrate versatility and accuracy of the present higher order plate bending element.

• Advances in aircraft and spacecraft science
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• v.6 no.5
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.