Element edge quadrature method for 4-node quadrilateral element for the evaluation of element stiffness matrix

This research paper focuses on the objective of developing a quadrature for evaluating the element stiffness matrix for the four-node quadrilateral element in finite element analysis (FEA). The proposed integration scheme is defined as an element edge method (EEM), which mimics the Gauss numerical integration scheme. This integration scheme consists of five sampling points and weights where four integration point locations are at the edges and one is at the center of the quadrilateral element. The proposed quadrature scheme has been tested using various benchmarked problems designed by various researchers to study the convergence of the results, accuracy of results, and stability of values.

A sampling point quadrature method for 3-node triangular element for the evaluation of element stiffness matrix in finite element analysis

Recently, many literature studies have focused on the development on new elements in finite elements. This paper aims to develop a new quadrature for the 3-node triangular element for the purpose of evaluation of element stiffness matrix. The analysis of triangular element is usually done in a quadrilateral element by dividing the quadrilateral element into two. The edge sampling point quadrature is a mimics of Gauss numerical integration scheme. This sampling integration scheme consists of five sampling points and weights where four sampling points are at the edge and one at the center of the element. Accuracy of results, convergence of the results and stability of values have been tested using the standard benchmarked problems defined by various research studies.

Modeling, Analyses, and Optimization of Planar Active Frame Structures Composed of Piezoelectric Beams

Frame structures are widely used in engineering applications, especially in space structures. For special use such as shape and vibration control of such structures, piezoelectric patches are usually placed on the beam surfaces to form active frame structures. To perform shape control or vibration control tasks, modeling methods for the formed active frame structures need to be studied. This paper develops a new distributed model of an active frame structure composed of multilayer piezoelectric beam components. First, the governing equations of a beam, bonded with piezoelectric patches, are developed via the generalized Hamilton principle, by considering the transverse shear strain. Then, the analytical solutions of the governing equations and the generalized element stiffness matrix are derived through the distributed transfer function formulation. Finally, the analytical solution of the entire system is obtained by the technique for assembling element stiffness matrix. In numerical simulations, buckling and vibration of an active frame structure are both studied. In addition, a novel Improved Ant Lion algorithm is proposed for optimal design of the frame structures. The optimization examples confirm that the proposed algorithm is more efficient than other existing popular algorithms such as Genetic Algorithm (GA) and Ant Lion Optimization (ALO) algorithm.

Combined Hybrid Finite Element Method Applied in Elastic Thermal Stress Problem

In view of combinative stability, combinative variational principle based on domain decomposition for elastic thermal stress problem is constructed with the merits of avoiding Lax–Babuska–Brezzi (LBB) conditions. Compared with the principle of elasticity problem, new load items from thermal are involved. In addition, combined hybrid finite element is proposed to discretize the new principle and to formulate element stiffness matrix. Energy compatibility is introduced not only to simplify the variational principle and the corresponding element stiffness matrix but also to reduce the error of finite element solutions. On cuboid element, the energy compatible stress mode is given explicitly. The numerical results indicate that combined hybrid element with eight nodes can give almost the same computing accuracy of displacement and better computing accuracy of stress compared with cuboid element with 20 nodes, is not sensitive to mesh distortion and can circumvent Poisson-locking phenomenon.

Simple and Accurate Eight-Node and Six-Node Solid-Shell Elements with Explicit Element Stiffness Matrix Based on Quasi-Conforming Element Technique

Based on the quasi-conforming (QC) element technique, accurate and reliable eight-node and six-node solid-shell elements are presented in this paper. These QC solid-shell elements can alleviate shear and Poisson thickness locking by appropriately interpolating the strain fields over the element domain, and they are completely free from hourglass modes by ensuring the rank sufficiency of the element stiffness matrix a priori. Furthermore, the element stiffness matrices of the present elements are evaluated explicitly rather than resorting to the numerical integration, which leads to a high computational efficiency. The QC solid-shell elements with the properly interpolated element strain fields can rigorously pass both membrane and bending patch tests. The popular benchmark problems are used to evaluate the performance of the QC solid-shell elements. The numerical results show that the present QC solid-shell elements yield not only accurate displacements but also good stress results for all the stress components. Particularly, the present QC solid-shell elements are capable of giving quite accurate results even with very coarse mesh.