Analytical Displacement And Traction Kernels For Dynamic BEM Analysis Of Plates

This paper presents the derivations and final analytical expressions for the displacement and traction collocation based particular solutions for dynamic analysis of plate bending problems. It is well known that these expressions represent the core of the dynamic analysis (whether forced or free vibrations) using the so-called dual reciprocity boundary element method or mass matrix approach. The shear deformable plate bending theory according to Reissner is used. The derived expressions are firstly derived via operator decoupling technique in terms of any arbitrary approximation functions (i.e. general expressions). Then suitable expressions corresponding to the thin plate spline function are derived. It was found that these functions are singular. A new proposed analytical smoothing scheme is introduced. This scheme is based on cancelling such singularity by adding suitable complementary singular fundamental solution. The new complementary singular solution is derived using another decoupling procedure and the final smooth forms for the spline displacements and tractions are presented.