An edge center-based strain-smoothing triangular and tetrahedral element for analysis of elasticity

Abstract

A novel edge center-based strain-smoothing method is put forward and applied to triangular and tetrahedral finite elements for linear and geometric nonlinear analysis of elastic mechanics. In the proposed edge center-based strain-smoothing element (EC-SSE), the linear strain field is constructed accordingly to the smoothed strain at element edge centers or face centers. The smoothed strain at both triangular and tetrahedral element edge centers is obtained directly utilizing elements adjacent to the edge, without requiring smooth domain. Besides, the smoothed strain at edge centers is averaged and assigned to the face center for tetrahedral elements. Compared with other methods, EC-SSE not only constructs a linear strain field within elements without introducing extra DOFs, but also ensures the strain consistency at the centers of intersecting edges or interfaces, which help to tremendously improve the smoothness of strain/stress distribution in the whole field. The EC-SEE passes basic element tests, including standard patch test, zero energy mode and linear independent tests. Subsequently, some attractive performances of EC-SSE, such as high accuracy and convergence rates for both displacement and strain energy, smoother stress field and the absence of temporal instability problems, are demonstrated through a variety of practical numerical examples.