Contact Analysis for Solids Based on Linearly Conforming Radial Point Interpolation Method

Abstract

To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS ® and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids.

A superconvergent point interpolation method (SC‐PIM) with piecewise linear strain field using triangular mesh

“…The displacement at any point in a cell is first approximated via point interpolation using Equation (17). The strains at points k,P and I are then evaluated using Equations (19) and (20). The strain field is next constructed again via point interpolation using Equation (18).…”

“…It is formulated based on the generalized Galerkin weak form and the PIM shape functions constructed employing point interpolation procedure using a small set of nodes located in a local support domain that can be overlapping [9,10]. A more general form called LC-RPIM [19,20] is also developed based on the radial PIM that uses radial basis functions and hence works well for extremely irregular node distributions [10,14]. A good feature of PIM and RPIM shape functions is that they possess Delta function property, which allows straightforward imposition of essential boundary conditions.…”

Certified solutions for hydraulic structures using the node‐based smoothed point interpolation method (NS‐PIM)

“…More important, the NS-PIM can obtain an upper bound solution in energy norm for elasticity problems with homogeneous essential boundary conditions [16,17]. Owing to the excellent properties, the NS-PIM (and NS-RPIM [18]) has been further developed for conducing the adaptive analysis [19], the contact problems [20], the heat transfer and the thermoelasticity problems [21,22] and provides upper bound solutions in energy norm as it does for elasticity problems.…”

A diagonal offset algorithm for the polynomial point interpolation method

“…In this method, local supporting nodes are selected based on background cells and the moment matrix never becomes singular for non-coinciding nodes. Zhang et al [13] extended LC-PIM for 3-D elasticity problems and Li et al [14] used the same method for the contact analysis of solids.…”