A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties

An 8-node solid element is developed based on the partition of unity method. The formulation uses isoparametric shape functions of the classical 8-node solid element to form the partition of unity and a modified least squares shape functions based on the point interpolation method for the local approximation. The motivation for the formulation is to obtain an element that ensures both inter-element compatibility and completeness properties. An element that simultaneously satisfies both these properties is capable of good performances under distorted mesh shapes. This is reflected in the numerical experiments reported in this paper.