A variational framework for the strain-smoothed element method
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Recently, the strain-smoothed element (SSE) method has been developed for the finite element analysis of solids and shells. Although the SSE method has been verified to show improved convergence behaviors compared to other strain smoothing methods in various numerical examples, there has been no theoretical evidence for the convergence behavior. In this paper, we establish a mathematical foundation for the SSE method. We propose a mixed variational principle in which the SSE method can be interpreted as a Galerkin approximation of that. The proposed variational principle is a generalization of the well-known Hu–Washizu variational principle, and various existing methods such as smoothed finite element methods can be expressed in terms of the proposed variational principle. With a unified view to the SSE method and other existing ones through the proposed variational principle, we analyze the convergence behavior of the SSE method and explain the reason for improved performance compared to others. Numerical experiments that support our theoretical results are presented.
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