A robust triangular membrane element

Abstract

To analyze the plane problem with irregular mesh and complicated geometry, it is helpful to utilize the triangular element. In this study, several optimization criteria will be elaborated. By utilizing these provisions and satisfying the equilibrium conditions, a novel triangular element, named SST, is developed. To demonstrate the high accuracy and efficiency of the new element, a variety of structures will be solved. The findings will prove that the presented element has a low sensitivity to the geometric distortion. Moreover, the parasitic shear error will not arise when this element is employed. In addition to these, the proposed element is rotational invariant. Comparison studies will reveal that the SST element is more robust than the other well-known triangular ones.

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

“…It is also realized that RF 4 is exactly similar to the formulations in Refs. [35 , 36] . Upon comparison, it is seen that the degree of freedom is shared among the normal strain components in RF 3 , which could be one of the causes for the inaccuracies in solving the thick curved beam and Cook's tapered beam problems, apart from being a shortage of one degree of freedom.…”

“…The effect of independence of degrees of freedom on the simulation results is further evidenced by the performance of RF 3 as compared to the finite elements in Refs. [35 , 36] or RF 4 .…”

Geometrical nonlinear analysis by plane quadrilateral element

“…Accordingly, strain interpolation field can be written in the matrix form as follows: (14) . q  ε B q (15) 0 0 0 1 0 0 0 0…”

“…Structures which have irregular geometry can be easily meshed with the help of four-node elements. By employing strain gradient notation tactic, optimality constraints such as insensitivity to geometric distortion, rotational invariant, satisfying equilibrium equations and elimination of the parasitic shear error can be included into the formulation of the element [12][13][14][15]. To extend these properties into geometrical nonlinear problems, corotational technique is deployed.…”