Optimal frequency design of tower structures via an approximation concept

The purpose of this paper is to develop a new numerical method via an approximation concept for finding the optimal bending stiffness distribution of a one-dimensional distributed-parameter structure (i.e. beam) under a fundamental natural frequency constraint. The distributed-parameter structure 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. Then the displacement function is 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 stiffnesses can be obtained from a set of simultaneous linear equations which is rearranged from a set of governing equations of the lowest eigenvibration. No iteration is required in determining the optimal displacement functions and bending stiffnesses. A numerical example of a tower structure is presented in order to demonstrate the validity, efficiency and accuracy of this method.

[1]  W. Prager Conditions for structural optimality , 1972 .

[2]  Takashi Yamane,et al.  Optimum design and earthquake-response constrained design of elastic shear buildings , 1986 .

[3]  Robert Levy,et al.  Recent Developments in Structural Optimization , 1987 .

[4]  Frithiof I. Niordson,et al.  On the optimal design of a vibrating beam , 1965 .

[5]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints , 1988 .

[6]  Bion L. Pierson,et al.  A survey of optimal structural design under dynamic constraints , 1972 .

[7]  V. B. Venkayya,et al.  Structural optimization: A review and some recommendations , 1978 .

[8]  J. E. Taylor,et al.  Minimum mass bar for axial vibration at specified natural frequency. , 1967 .

[9]  Izuru Takewaki,et al.  Hybrid Inverse Mode Problems for FEM-Shear Models , 1995 .

[10]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints - A review , 1992 .

[11]  M. Turner,et al.  Design of minimum mass structures with specified natural frequencies. , 1967 .

[12]  William Prager,et al.  Problems of Optimal Structural Design , 1968 .

[13]  M. W. Dobbs,et al.  Application of optimality criteria to automated structural design , 1976 .

[14]  L. A. Schmit,et al.  Structural synthesis - Its genesis and development , 1981 .

[15]  Niels Olhoff,et al.  Maximizing Higher Order Eigenfrequencies of Beams with Constraints on the Design Geometry , 1977 .

[16]  George J. Simitses,et al.  Optimal beam frequencies by the finite element displacement method , 1973 .

[17]  B. L. Karihaloo,et al.  Optimum design of vibrating cantilevers , 1973 .

[18]  Makoto Ohsaki,et al.  Sequential optimal truss generator for frequency ranges , 1988 .

[19]  C. Sheu,et al.  Elastic minimum-weight design for specified fundamental frequency☆ , 1968 .

[20]  E Atrek,et al.  New directions in optimum structural design , 1984 .