• Steel and Composite Structures
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• v.23 no.1
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• pp.41-51
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• 2017

A $C^0$ FE model developed based on an efficient higher order zigzag theory is used for hygrothermal analysis of laminated composite plates. The $C^0$ FE model satisfies the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of $C^1$ continuity associated with the above plate theory. In the present theory the above mentioned $C^0$ continuity of the present element is compensated in the stiffness matrix formulation by using penalty parameter approach. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature/moisture fields (initial strains) must be consistent with total strain field. Special steps are introduced by field consistent approach (e.g., sampling at gauss points) to compensate this problem. A nine noded $C^0$ continuous isoparametric element is used in the proposed FE model. Comparison of present numerical results with other existing solutions shows that the proposed FE model is efficient, accurate and free of locking.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.475-484
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• 2000

In this paper, new additional nonconforming modes for the improvement of bending behavior in the distorted 8 node hexahedral element and their effective modification method are studied. The rotational degrees of freedom are introduced by using a functional in which the rotations are independent variables. In an element formulation, the same interpolations are used in displacement and rotation fields, but nonconforming modes we applied only in displacement fields. To verify the developed element various numerical tests are carried out and test results show good behavior.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.47-64
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• 2015

This paper presents the effect of hybridization material on variation of critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the principle of virtual displacement; the formulation is based on a new trigonometric shape function of displacement taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.393-417
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• 2015

In this paper an 8-node quadrilateral assumed stress hybrid Mindlin plate element with $39{\beta}$ is presented. The formulation is based on complementary energy principle. The proposed element is free of shear locking and is capable of passing all the patch tests, especially the non-zero constant shear enhanced patch test. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is successfully used to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. Particularly, in order to improve element's accuracy, the assumed stress field is derived by employing $39{\beta}$ rather than conventional $21{\beta}$. The resulting element can be adopted to analyze both moderately thick and thin plates, and the convergence for the very thin case can be ensured theoretically. Excellent element performance is demonstrated by a wide of experimental evaluations.

• Steel and Composite Structures
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• v.18 no.3
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• pp.673-691
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• 2015

In this paper we are particularly focusing on the dynamic crack fatigue life of a 25 m length wind turbine blade. The blade consists of composite materiel (glass/epoxy). This work consisted initially to make a theoretical study, the turbine blade is modeled as a Timoshenko rotating beam and the analytical formulation is obtained. After applying boundary condition and loads, we have studied the stress, strain and displacement in order to determine the critical zone, also show the six first modes shapes to the wind turbine blade. Secondly was addressed to study the crack initiation in critical zone which based to finite element to give the results, then follow the evolution of the displacement, strain, stress and first six naturals frequencies a function as crack growth. In the experimental part the laminate plate specimen with two layers is tested under cyclic load in fully reversible tensile at ratio test (R = 0), the fast fracture occur phenomenon and the fatigue life are presented, the fatigue testing exerted in INSTRON 8801 machine. Finally which allows the knowledge their effect on the fatigue life, this residual change of dynamic behavior parameters can be used to predicted a crack size and diagnostic of blade.

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.1
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• pp.9-13
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• 2009

A simple outline for teaching adaptive scheme based finite element method for planar problems as a part of computer aided teaching of structural engineering curriculum is presented. Displacement based finite element formulation for planar problems and representative strain value based adaptive scheme for mesh generation are considered. As examples, a cantilever beam with a concentrated load treated as a planar problem and stretching of a plate with a circular hole are analyzed with displacement based finite element method with adaptive meshes. The examples and outlines show how adaptive based finite element method may become an essential part of computer aided teaching of structural engineering.

• Steel and Composite Structures
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• v.34 no.2
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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.

• Structural Engineering and Mechanics
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• v.18 no.2
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• pp.247-262
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• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• 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.