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This paper deals with the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges. The analysis is carried out using variable thickness finite strips based on Mindlin‐Reissner assumptions which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined. Results are presented for a series of problems including plates and stiffened panels. In a companion paper these accurate and inexpensive finite strips are used in the context of structural shape optimization.

The purpose of this paper is to develop a computational technique to couple finite element and meshfree methods for locking‐free analysis of shear deformable beams and plates, and to impose the boundary conditions directly when the matching field approach is adopted in the meshfree region.

Matching field approach eliminates shear‐locking which may occur due to inconsistencies in the approximations of the transverse displacement and rotation fields in shear‐deformable beams and plates. Continuous blending method is modified in order to be able to satisfy the constraint conditions of the matching field strategy.

For both transverse displacement and rotation fields, the developed technique produces approximation functions that satisfy the Kronecker delta property at the required nodes of the meshfree region when the matching field approach is adopted.

This approach allows for direct assembly of the stiffness matrices that are built for separate finite element and meshfree regions when the matching field approach is adopted. The boundary conditions can be directly applied, and the reaction forces can also be calculated directly from the structural stiffness matrix by using the developed technique.

In the present investigation, a finite element analysis procedure is developed to predict the initiation and propagation of damages as well as to analyse damaged laminated composite plates under forced vibration and impact loads. Isoparametric quadratic plate bending element (nine‐noded rectangular) based on Mindlin plate theory is used to develop the FE codes for the present analysis. A phenomenological damage model assuming the effective stress concept is used to represent the damage of a lamina. The initiation and progress of damage due to forced vibration and low velocity impact are studied for different impactor velocities.

The aim of this paper is to investigate the initiation and progress of damage in laminated composite shells at elevated moisture concentration and temperature due to low‐velocity impacts.

A finite element analysis procedure is developed to investigate the initiation and propagation of damage in laminated composite shells in hygrothermal environments.

It was found inter alia, that in the case of rise of temperature present FEM results match well with closed form solutions and that stress results at different levels of moisture concentration agree with the results published in the open literature.

The paper provides in‐depth insight into the progress of damage in laminated shell structures.

The paper investigates initiation and progress of damage in laminated composite shell structures due to low‐velocity impacts.

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.

A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.

The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.

Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.

The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.

These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

Topology optimization and conventional structural sizing optimization procedures are used together to obtain optimum designs for plate structures. A three‐layer, Mindlin‐Reissner plate model is first used with topology optimization to determine optimal stiffening zones. The central layer represents the unstiffened plate and the symmetrically located upper and lower layers are potential stiffening zones. A stiffening volume is specified and the objective is to minimize the strain energy. From these stiffening zones, a set of centre lines of equivalent stiffening Timoshenko beam elements is selected. A sizing optimization procedure is then used to optimize the stiffener dimensions. The objective of the design in the final sizing optimization stage is to minimise the strain energy keeping the total stiffened plate volume constant. The efficiency and accuracy of the proposed strategy is illustrated through several applications.

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

Two isoparametric Lagrangian shallow shell elements are presented: a 4‐node element QUAD4 and a 9‐node element QUAD9. These elements are based on Mindlin/Reissner plate elements as described in a series of papers. These elements are sophisticated by adding conventional membrane stiffness and membrane‐bending coupling terms based on Maguerre's approximate shallow shell theory. This results in double curved shell elements which originally possess severe membrane locking behaviour. This defect is overcome in the same way as the shear locking problem is solved.