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This paper presents a new 9 DOF triangular element for plate bending. It is an analytically integrated improved version of the simplest member in the hierarchy of numerically integrated elements. These elements have been based on the so‐called Hybrid—Trefftz model (HT), a recently developed hybrid model associated with enforcing interelement continuity on locally based displacement fields chosen such that they a priori verify the Lagrange plate equation over the element. In the process of development of the element stiffness matrix in a standard HT model, one has to invert the so‐called natural stiffness matrix, a 7 × 7 matrix associated with the expression of the strain energy in terms of the Trefftz's functions of the element. The inversion of this fully populated matrix represents the most expensive part of the calculation of the element. The basic improvement of the standard Hybrid—Trefftz 9 DOF triangle consists in replacing the original Trefftz's functions by new ones which are energy orthogonal and consequently, result in a diagonal natural stiffness matrix. This not only alleviates considerably the computer cost, but also significantly simplifies the algebra making analytical integrations possible. The practical efficiency of the new element which passes the patch test is demonstrated through numerical examples including the difficult simply supported skew plate problem with a strong singularity at its 150° obtuse corner.

The purpose of this paper is to propose a new finite element method (FEM) solving strategy for efficient analysis of the challenging edge effect problem in plate structures. Its main ideas are to develop special-purpose plate element models to effectively simulate the behaviors in the plate’s edge zones near free/SS1 edges.

These new elements are developed based on the hybrid-Trefftz element method. During their construction procedures, the analytical solutions of the edge effect problem, which are in exponential forms, are used to enhance the interior displacement fields. Besides, the Lagrangian multipliers are introduced into the modified hybrid-Trefftz functional for considering the stress resultant constraints at free/SS1 edges. Thus, these elements theoretically possess the abilities to correctly capture the very steep gradients of the resultant distributions in the boundary layers.

These new specialized hybrid-Trefftz plate elements can very efficiently solve the edge effect problem with high accuracy, even when distorted meshes are used. Moreover, because these elements’ construction procedures contain only boundary integrals, the computation expense for accurately integrating the exponential trial functions can be considerably saved.

This work presents an alternative novel idea for using the FEM to more effectively handle the local stress problems by incorporating the use of the analytical trial functions.

The purpose of this paper is to develop a hybrid‐Trefftz (HT) finite element model (FEM) for simulating heat conduction in nonlinear functionally graded materials (FGMs) which can effectively handle continuously varying properties within an element.

In the proposed model, a T‐complete set of homogeneous solutions is first derived and used to represent the intra‐element temperature fields. As a result, the graded properties of the FGMs are naturally reflected by using the newly developed Trefftz functions (T‐complete functions in some literature) to model the intra‐element fields. The derivation of the Trefftz functions is carried out by means of the well‐known Kirchhoff transformation in conjunction with various variable transformations.

The study shows that, in contrast to the conventional FEM, the HT‐FEM is an accurate numerical scheme for FGMs in terms of the number of unknowns and is insensitive to mesh distortion. The method also performs very well in terms of numerical accuracy and can converge to the analytical solution when the number of elements is increased.

The value of this paper is twofold: a T‐complete set of homogeneous solutions for nonlinear FMGs has been derived and used to represent the intra‐element temperature; and the corresponding variational functional and the associated algorithm has been constructed.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present a novel formulation in the framework of assumed stress quasi-conforming method for the static and free vibration analysis of anisotropic and symmetric laminated plates.

Firstly, an initial stress approximation ruled by 17 parameters, which satisfies the equilibrium equations is derived to improve the performance of the constructed element. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions for strain integration.

Several numerical examples are presented to show the performance of the new element, and the results obtained are compared with other available ones. Numerical results have proved that the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

This paper proposes a new QC element for the static and free vibration analysis of anisotropic and symmetric laminated plates. In contrast with the complicated analytical solutions of the equilibrium equations, an initial stress approximation ruled by 17 parameters is adopted here. The Timoshenkos laminated composite beam functions are introduced as boundary string-net functions for strain integration. Numerical results demonstrate the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999–2002.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

This paper aims to present an extension of two recently published elements (which are based on Petrov‐Galerkin formulation) to geometric nonlinear (GNL) problems.

Two different sets of shape functions, namely isoparametric and metric, suitably chosen to satisfy the necessary compatibility and completeness conditions, are used as test and trial functions, respectively. Total Lagrangian formulation is used for the implementation of the element.

In implementing the unsymmetric formulation for nonlinear problems, the deformation gradient tensor can be evaluated invariably using either isoparametric or metric shape functions. The developed elements are found to exhibit improved performance in the presence of mesh distortions.

The numerical problems in this paper involve linear elastic materials.

Extension of US‐QUAD8 and US‐HEXA20 for GNL problems is new.

The purpose of this study is to develop an elasto-plastic multi-material shell model by which finite element analysis of laser welded joints is carried out at the interface of the heat-affected zone and base material.

The multi-material shell model is implemented on the simple cantilever and double cantilever welded plates to examine the efficiency of the developed model.

By reducing the computational time approximately 20 times with the developed model, the results obtained in the form of von Mises stress and equivalent plastic strain are found in good agreement as compared with the reference solid model.

The accurate and fast prediction of the stresses and strains in the laser welded joints, and the developed multi-material model is helpful to simulate complex industrial welded structures.