The partitioned element method in computational solid mechanics

• Published in: Computer methods in applied mechanics and engineering 2012-09, Vol.237-240, p.152-165
• Main Authors: Rashid, M.M., Sadri, A.
• Format: Article
• Language: English
• Subjects: Approximation; Convergence; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Partitioned element method; Physics; Polygonal elements; Robustness; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2012.05.014

► We propose a new formulation for polygonal finite elements of general shape. ► The method rests on a partition of the element into quadrature cells. ► Shape functions are approximated as piecewise-linear on the quadrature cells. ► The new method is robust with respect to element geometric pathologies. ► The new method exhibits performance similar to conventional finite elements. A finite-element-like approximation method is proposed for solid-mechanics applications, in which the elements can take essentially arbitrary polygonal form. A distinguishing feature of the method, herein called the “partitioned element method,” is a partitioning of the elements into quadrature cells, over which the shape functions are taken to be piecewise linear. The gradient and constant values for each cell are determined by minimizing a quadratic function which represents a combined smoothness and compatibility measure. Linear completeness of the shape-function formulation is proved. Robustness in the presence of element non-convexity and geometric degeneracy (e.g. nearly coincident nodes) are particular goals of the method. Convergence for various 2D linear elasticity problems is demonstrated, and results for a finite-deformation elastic–plastic problem are compared to those of the standard FEM.