Preprint Article Version 1 This version is not peer-reviewed

A Modified Cell-Based Strain Smoothing for Material Nonlinearity

Version 1 : Received: 6 December 2019 / Approved: 7 December 2019 / Online: 7 December 2019 (01:51:23 CET)

How to cite: Lee, C.K.; Natarajan, S. A Modified Cell-Based Strain Smoothing for Material Nonlinearity. Preprints 2019, 2019120091 (doi: 10.20944/preprints201912.0091.v1). Lee, C.K.; Natarajan, S. A Modified Cell-Based Strain Smoothing for Material Nonlinearity. Preprints 2019, 2019120091 (doi: 10.20944/preprints201912.0091.v1).

Abstract

This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

Subject Areas

cell-based smoothed finite element method; quadratic triangular element; linear smoothing function; hyperelasticity

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