A novel assumed-strain finite element for detecting the elastic behavior of wall-like structures

Abstract

It is aimed to propose a new triangular plane finite element to improve the accuracy and reduce the computational effort for analysis of plane structures. The suggested element is formulated by assuming an incomplete second-order strain field. It leads to an element free from shear parasitic error with lower sensitivity to the mesh distortion. Satisfying both equilibrium and compatibility equations in the strain field level results in 12 independent strain states. Accordingly, the suggested element has 12 degrees of freedom, which are allocated to six nodes. Although the suggested element has the geometry and number of degrees of freedom same as the well-known linear strain triangular element, but its accuracy and efficiency are much better than many of the available high-performance membrane elements. The selected geometry provides the opportunity to simply include the presented element in the general finite element analysis software. After evaluation of the element performance using basic benchmark problems, to demonstrate the efficiency of the proposed formulation in comparison with widely used finite elements, different shear and retaining wall structures are analyzed by the developed element. The attained results for even coarse meshes prove higher accuracy and efficiency of the developed element in computation of displacements and stresses. Another advantage of the proposed element in comparison with the other available robust finite elements is its simple and straightforward formulation.

Keywords:

• Triangular membrane element
• assumed strain formulation
• insensitivity to mesh distortion
• wall-like structures