TREATMENT OF HYPERSINGULARITIES IN BOUNDARY ELEMENT ANISOTROPIC PLATE BENDING PROBLEMS

Abstract

THIS PAPER PRESENTS AN APPROACH FOR ANISOTROPIC THIN-PLATE BENDING PROBLEMS USING THE BOUNDARY ELEMENT FORMULATION WHEN THE SOURCE POINTS ARE LOCATED ON THE BOUNDARY AND RESULTING HYPERSINGULARITIES ARE ANALYTICALLY TREATED. WHEN THE INTEGRATION IS CARRIED OUT WITH THE SOURCE AND FIELD POINTS BELONGING TO THE SAME ELEMENT THE RADIUS BETWEEN THEM GOES TO ZERO, LEADING TO THE SINGULAR INTEGRATION. THE ANISOTROPIC FUNDAMENTAL SOLUTION FOR THE PLATE BENDING HAS A SINGULARITY OF R^(-2) ORDER. THUS, UNDER THESE CONDITIONS, HYPERSINGULARITIES TREATMENT CAN NOT BE AVOIDED. THE USED BOUNDARY ELEMENT FORMULATION INCLUDES TWO BOUNDARY INTEGRAL EQUATIONS WHERE REGULAR, WEAK SINGULAR, STRONG SINGULAR AND HYPERSINGULAR INTEGRALS ARE FOUND. THIS WORK PROVIDES A PROCEDURE FOR THE TREATMENT OF STRONG AND HYPERSINGULAR INTEGRALS. ALL TERMS OF THE ANALYTICAL INTEGRATIONS ARE GIVEN FOR CONSTANT ELEMENTS. NUMERICAL EXAMPLES FOR LAMINATE COMPOSITE MATERIALS UNDER TRANSVERSELY UNIFORM DISTRIBUTED LOAD ARE PRESENTED. THE ACCURACY OF THE PROPOSED APPROACH IS ASSURED BY COMPARISON WITH ANALYTICAL AND ¯NITE ELEMENT RESULTS AVAILABLE IN THE LITERATURE.