# An Interior-Constraint BEM for Regularization of Problems with Improper Boundary Conditions

Document Type : Regular Article

Authors

1 Assistant Professor, Department of Civil Engineering, Penn State Harrisburg, Middletown, PA 17057, USA

2 Associate Professor, Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA

3 Professor, Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA

Abstract

A well-posed problem in the analysis of elastic bodies requires the definition of appropriate constraints of the boundary to prevent rigid body motion. However, one is sometimes presented with the problem of non-self-equilibrated tractions on an elastic body that will cause rigid body motion, while the boundary should remain unconstrained. One such case is the analysis of multi-particle dynamics where the solution is obtained in a quasi-static approach. In such cases, the motion of the particles is governed by the dynamic equilibrium while the contact forces between particles may be computed from elastostatic solutions. This paper presents two regularization methods of Interior-Constraint Boundary Element techniques for elastostatic analysis with improper boundary supports. In the proposed method rigid body modes are eliminated by imposing constraints on the interior of an elastic body. This is accomplished through simultaneously solving the governing Boundary Integral Equation and Somigliana’s Identity. The proposed method is examined through assessment and verification studies where it is demonstrated, that for all considered problems rigid body motion is successfully constrained with minimal effects on body deformations.

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### History

• Receive Date: 28 November 2017
• Revise Date: 11 January 2018
• Accept Date: 11 January 2018