Analysis of Uniform-Strength Shape by the Growth-Strain Method. Application to the Problems of Steady-State Vibration.

Abstract

The growth-strain method, developed using the finite-element calculation of the deforming of shapes produced by swelling and contracting of itself, was previously proposed as a shape optimization method. The present report describes an application of the growth-strain method to the problems of steady-state vibration. In particular, free vibration with a normal mode and vibrational response to a harmonic excitation are considered. A difference of the implementation of the method for these vibration problems from that for static problems lies in analyzing the stress distribution at the deformation in the normal mode or in the amplitude of the vibrational response. Numerical examinations are carried out on simple beam structures. In these examinations, the growth-strain method shows a feasibility even in the optimization of structures under dynamic circumstances.