Semi-explicit optimal frequency design of chimneys with geometrical constraints

Abstract

The purposes of this paper are to develop a new finite-element-based optimal design method for chimneys under a fundamental natural frequency constraint and geometrical constraints (minimum stiffness constraints) and to apply this method to practical chimney design. The chimney is modeled by an FEM system and the bending stiffness distribution is approximated by a piecewise-linear function. A cubic displacement function is utilized in the FEM system. The displacement function is then determined so that the optimality condition described at every point would be satisfied only at the element ends. It is shown that the optimal bending stiffness in the interval with stiffness greater than the given lower bound and the lowest-mode displacements in the interval with the lower-bound stiffness can be obtained semi-explicitly from a set of simultaneous linear equations which is rearranged from a set of governing equations of the lowest eigenvibration. In order to identify the elements with lower-bound stiffnesses, a procedure based on inverse mapping is utilized. Several numerical examples are presented in order to demonstrate the validity and efficiency of this method.