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The purpose of this paper is to get a more consistent finite element description for three-dimensional (3D) Timoshenko beam elements. It extends the common description of beam elements by modifying the shape functions and considers the warping of the cross-section due to torsion.

The paper builds mainly on a finite element description of 3D Timoshenko beam elements. The implementation of high-order shape functions for torsion is done by adding a seventh degree of freedom to the system.

The results reveal that for some beams, depending on their physical dimensions, the warping of the cross-section has large influence. In comparison to a conventional FE program, the extended finite element description considers the warping and yields more accurate results.

An application of the extended finite element description is done with an implementation of the code in MATLAB. The static and dynamic behavior of a rotor in an electrical machine is investigated.

This paper presents a more consistent finite element description of 3D Timoshenko beam elements considering the warping. A comparison to conventional finite element descriptions is given.

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.

First, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.

The proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.

This work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.

Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.

The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.

A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

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.

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.

Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties.

First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration.

The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy.

New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.

In this paper, three triangular flat shells developed by combining an excellent membrane element (OPT) with three outstanding plate bending elements (DKT, RDKTM and DST-BK), respectively, are used to study this phenomenon. Benchmark tests are implemented to evaluate the performance of three selected plate elements and the formulated flat shells.

The inter-element coupling effect of membrane and plate components belonging, respectively, to two adjacent shells deteriorate the performance of shells. Therefore, a shell’s performance cannot be guaranteed certainly by the superimposed membrane and plate behaviors.

The “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

Previous studies mainly focus on formulation of high-performance membrane and plate elements. However, the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary, has attracted less attention. Thorough benchmark tests for three flat shells are implemented to investigate the phenomenon. The results shows that the inter-element coupling effect deteriorates the performance of shells. And the “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.

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.

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 present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.