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A finite element formulation for flexure of isotropic plates based on a recent refined theory is developed. The refined theory incorporates effects of transverse shear, transverse normal stress and transverse normal strain. The Galerkin finite element method was used to develop the finite element equations for both plate bending and inplane problems. The performance of the proposed finite element model was evaluated by solving problems of uniformly loaded thick plates with different support conditions. The results of the present formulation are compared with Mindlin/Reissner and elasticity solutions.

A formulation has been developed for thermo‐elastoviscoplastic finite element analyses of continuous fibre‐reinforced composite plates subject to bending loading using a generalized continuum mechanics approach. Such an approach is used to model the non‐homogeneity in a composite, which is constituted by fibres embedded in a matrix material. The present formulation computes the respective stresses occurring in each constituent so that the respective yield criterion and flow rule of each constituent may be used if there is a material yielding in any constituent. Thermo‐elastic deformation of fibre and thermo‐elastoviscoplastic deformation of matrix are considered in the present study because the yield strength of fibre is substantially higher than that of matrix in many cases. Both constituents are assumed to be isotropic so that the von‐Mises yield criterion may be used for viscoplastic yielding of matrix. As numerical examples, a parametric study is performed for thermo‐elastoviscoplastic deformations of laminated composite plates subject to thermal bending loads.

This paper aims to describe the formulation of a new finite element by assuming the strain field rather than the displacement field and by using the Reissner–Mindlin plate theory for the free vibration analysis of bending plates. This quadrilateral element consists of four-nodes and twelve degrees of freedom. The suggested element is based on assumed functions of the strain field that satisfy the compatibility equation.

After the proposition of the new element, several numerical tests for plates with regular and distorted meshes are presented to assess the performance of the new element. In addition, a parametric study is carried out to analyze the effects of biaxial loads on the natural frequencies of square plates with various boundary conditions. Detailed discussions are proposed after each benchmark problem.

The formulated element has verified the shear locking test and passes the patch test. The obtained results from the developed element show an excellent accuracy and fast convergence, and the natural frequencies are in excellent agreement when compared with analytical and other available numerical solutions.

The present element is simple in its formulation and has been proven to be applicable to thin or thick plate situations with sufficient accuracy. This element with full integration is free from shear locking, however, the numerical results provided by the standard four-node plate element R4 element show locking phenomena in thin plates. In addition to these features, the imposition of the compatibility conditions and the rigid body modes allow obtaining a finite element with higher-order terms for displacements field, which can increase the performance of the finite elements.

A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method.

This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary.

The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software.

This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.

The 4‐node assumed strain elements are among the best elements available today but the bending moments at their full integration points oscillate severely. This paper presents a one point integrated version of the 4‐node assumed strain plate element of Bathe‐Dvorkin. A Taylor series expansion approach is used to accommodate the linear variation of strains/stresses within the element and hence to stabilize the spurious zero energy modes. An extensive number of benchmark results are presented and compared.

It has been revealed that application of the differential form of Eringen’s nonlocal elasticity theory to some cases (e.g. cantilevers) leads to paradoxical results, and recourse must be made to the integral version of Eringen’s nonlocal model. The purpose of this paper, within the framework of integral form of Eringen’s nonlocal theory, is to study the bending behavior of nanoscale plates with various boundary conditions using the isogeometric analysis (IGA).

The shear deformation effect is taken into account according to the Mindlin plate theory, and the minimum total potential energy principle is utilized in order to derive the governing equations. The relations are obtained in the matrix-vector form which can be easily employed in IGA or finite element analysis. For the comparison purpose, the governing equations are also derived based on the differential nonlocal model and are then solved via IGA. Comparisons are made between the predictions of integral nonlocal model, differential nonlocal model and local (classical) model.

The bending analysis of nanoplates under some kinds of edge supports indicates that using the differential model leads to paradoxical results (decreasing the maximum deflection with increasing the nonlocal parameter), whereas the results of integral model are consistent.

A new nonlocal formulation is developed for the IGA of Mindlin nanoplates. The nonlocal effects are captured based on the integral model of nonlocal elasticity. The formulation is developed in matrix-vector form which can be readily used in finite element method. Comparisons are made between the results of differential and integral models for the bending problem. The proposed integral model is capable of resolving the paradox appeared in the results of differential model.

Presents the formulation of a new triangular finite element for plate bending. The element has 15 degrees of freedom: six displacements at the corners and midside nodes and nine rotations normal to the element side, three along each element side. The element is based on the Kirchhoff theory for plate bending and the shape functions are derived from a complete quartic polynomial. Presents a numerical assessment of the element, showing that the element passes the patch test and that it possesses a good converge rate. The stiffness matrix is integrated exactly.

This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates.

The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique.

Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation.

This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

The purpose of this paper is to apply the element decomposition method (EDM) in the study of the bending and vibration properties of plate and shell.

In the present method, each quadrilateral element is first divided into four sub-triangular cells, and the local strains are obtained in those sub-triangles based on linear interpolation. The whole strain filed is formulated through a weighted averaging operation of local strains, implying that only one integration point is adopted to construct the stiffness matrix. To reduce the instability of one-point integration and increase the accuracy of the present method, a stabilization item of the stiffness matrix is formulated by variance of the local strains. A mixed interpolated tensorial components (MITC) method is used in eliminating the shear locking phenomenon.

The novel EDM based on linear interpolation is effective in bending and vibration analyses of plate and shell, and the present method used in practical problems is reliable for static and free vibration analysis.

This method eliminated the instability of one-point integration and increased the accuracy by a stabilization item and performed stably in engineering analysis including large-scale problems of vehicle components.

The purpose of this paper is to propose a new four-node membrane element model with bending modification based on the equilibrium principle of element nodal internal forces and bending moments for the application of the one-step algorithm for bus rollover collision. And it can be concluded whether the proposed four-node membrane element model has practical value in engineering application or not.

Based on the equilibrium principle of element nodal internal forces and bending moments, the paper puts forward a four-node membrane element model with bending modification. A case study on the rollover of a typical bus body section is carried out by using the one-step algorithm for bus rollover collision to verify the effectiveness of the proposed element model.

For the simulation of bus rollover collision, the computational accuracy can be guaranteed, meanwhile, the calculated amount is much smaller than the shell element, and computational efficiency is improved significantly.

The proposed four-node membrane element model is used for the simulation of bus rollover collision for the first time. It holds the advantage of high computational efficiency of membrane element, and the computational accuracy is improved as well. In conclusion, it has some practical value in engineering application.