Separable Elements for Multi-dimensional Structures and Experimental Verifications

Description

Some structural elements must be investigated in three spatial dimensions resulting in a four dimensional problem when time is included. Four dimensional problems present particular difficulty due to the computational complexity. An efficient method is proposed to analyze the multidimensional problems using one dimension at a time. The new idea is a generalized discrete form of the well developed method of separable variables (in continuous functional form) in partial differential equations by which a multi-dimensional problem can be solved by some one dimensional problems analytically. Although the primary interest is in rectangular and polar domains, substructures or sub-domains being generated can be connected to other conventional elements to handle different shapes. Extensions to nonlinear structural dynamics will also be studied briefly. It is expected that the project will generate new phenomena which might not be possible due to the computational complexity, including localized linear 2D waves in bounded domains. Therefore, experimental verifications are essential.