The partitioned element method in computational solid mechanics

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.

► 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.