Equivalence between the Local Boundary Integral Equation and the Mean Value Theorem in the Theory of Elasticity

The boundary element method based on a boundary integral equation has been very successful in computational mechanics. Atluri et al. [4] recently developed a new meshless method using the local boundary integral equations. It eliminates the tedious step of mesh generation and thus greatly simplifies the numerical computation process. This paper shows the equivalence between the local boundary integral equation and the mean value theorem in the theory of elasticity. In addition, it gives new proofs for the mean value theorem of elasticity and its converse based on the concept of a companion solution.