Improved stiffness-based first-order approximations for structural optimization

Improved first-order approximations of displacements, stresses, and forces are presented. The main objectives in developing the method presented are 1) to preserve the ease of implementation and the efficiency of the common first-order approximations and 2) to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometrical changes and elimination of members. The method is based on results of a single exact analysis and can be used with a general finite element system. It is suitable for different types of design variables and structures. Results obtained by the proposed method are compared with various first-order approximations for modifications in the cross section as well as the geometry and the topology of the structure. It is shown that the proposed approximations are most effective in terms of the accuracy, the efficiency, and the ease of implementation.

[1]  J. Barthelemy,et al.  Two point exponential approximation method for structural optimization , 1990 .

[2]  M. F. Rubinstein,et al.  Automated Structural Synthesis Using a Reduced Number of Design Coordinates , 1973 .

[3]  H. Miura,et al.  An approximate analysis technique for design calculations , 1971 .

[4]  Moshe B. Fuchs,et al.  Linearized homogeneous constraints in structural design , 1980 .

[5]  Ramana V. Grandhi,et al.  Improved two-point function approximations for design optimization , 1995 .

[6]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[7]  Raphael T. Haftka,et al.  Recent Advances in Approximation Concepts for Optimum Structural Design , 1993 .

[8]  Raphael T. Haftka,et al.  Preliminary design of composite wings for buckling, strength and displacement constraints , 1979 .

[9]  C. Fleury.  First and second order convex approximation strategies in structural optimization , 1989 .

[10]  U. Kirsch.  Reduced basis approximations of structural displacements for optimaldesign , 1991 .

[11]  Uri Kirsch,et al.  Efficient sensitivity analysis for structural optimization , 1994 .

[12]  U. Kirsch,et al.  Approximate Behavior Models for Optimum Structural Design , 1981 .

[13]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[14]  Manohar P. Kamat,et al.  Approximate Reanalysis Methods , 1993 .

[15]  Uri Kirsch,et al.  Structural Optimization: Fundamentals and Applications , 1993 .

[16]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[17]  U. Kirsch,et al.  Exact structural reanalysis by a first-order reduced basis approach , 1995 .

[18]  Layne T. Watson,et al.  Two-point constraint approximation in structural optimization , 1987 .

[19]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[20]  U. Kirsch,et al.  Efficient reanalysis for topological optimization , 1993 .

[21]  Claude Fleury,et al.  Efficient approximation concepts using second order information , 1989 .

[22]  E. Salajegheh,et al.  New Approximation Method for Stress Constraints in Structural Synthesis , 1989 .