Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectang...

Various corotational schemes for solid, shell, bending plate and beam elements have been proposed so far. Nevertheless, this approach has rarely been utilized for membrane problems. In this paper, a new quadrilateral element will be suggested for solving nonlinear membranes. The simplicity, rapid convergence and high accuracy of the formulation are the three main characteristics of the presente...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

The need of polygonal elements to represent the domain is gaining interest among structural engineers. The objective is to perform static analysis and topology optimization of a given continuum domain using the rational fraction type shape functions of six node hexagonal elements. In this paper, the main focus is to perform the topology optimization of two-dimensional plate structures using Evo...

in this paper, two new quadrilateral elements are formulated to solve plane problems. low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the felippa pure bending test are characteristics of these suggested elements. one proposed element is formulated by establishing equilibrium equations for the second-order strain field. the other suggested...

In this paper, two new quadrilateral elements are formulated to solve plane problems. Low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the Felippa pure bending test are characteristics of these suggested elements. One proposed element is formulated by establishing equilibrium equations for the second-order strain field. The other suggested...

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathem...