16. The Singularity Method in Boundary Value Problems of the Theory of Elasticity
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概要
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Using the Maxwell-Betti's reciprocal theorem, the general formulation transforming the fundamental differential equation to the integral equation in the theory of elasticity is deduced. In similar ways as in hydrodynamics, boundary integral equations which are represented by either source and sink or doublet distribution are derived. The formulations of the boundary integral equation for various problems, i.e. the two dimensional elastostatics, the two dimensional elastodynamics, the three dimensional elastostatics and the plate bending problems are shown and studied especially regarding the property of their kernel function in concern with their numerical integration. To verify its usefulness and accuracy, some numerical examples are shown. The proposed equations are especially useful for stress concentration problems and diffraction problems during passage of elastic waves in the infinitely extended elastic medium.
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