Structural optimization by variational methods

This chapter contains notes for lectures delivered as part of the Advanced Study Institute “Computer Aided Optimal Design: Structural and Mechanical Systems” organized in Troia, Portugal, 30 June – 11 July 1986, by the Center of Mechanics and Materials of the University of Lisbon. The author gratefully acknowledges Professor Carlos Mota Soares and his collagues for a most successful arrangement of the meeting and the other lecturers for several extremely interesting contributions.

[1]  Z. Mroz,et al.  Column Design: Optimization of Support Conditions and Segmentation , 1977 .

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

[3]  Zenon Mróz,et al.  Optimal design of structures with variable support conditions , 1975 .

[4]  J. E. Taylor,et al.  Optimum design of a vibrating bar with specified minimum cross section. , 1968 .

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

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

[7]  Cheng Keng-Tuno,et al.  On non-smoothness in optimal design of solid, elastic plates , 1981 .

[8]  E. F. Masur Optimal structural design under multiple eigenvalue constraints , 1984 .

[9]  J. E. Taylor,et al.  The strongest column - An energy approach. , 1967 .

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

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

[12]  Raymond H. Plaut,et al.  Bimodal optimization of vibrating shallow arches , 1983 .

[13]  N. Olhoff,et al.  An investigation concerning optimal design of solid elastic plates , 1981 .

[14]  Andrej Cherkaev,et al.  Sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates , 1981 .

[15]  C. Popelar Optimal Design of Structures Against Buckling: A Complementary Energy Approach , 1977 .

[16]  William Prager,et al.  A note on optimal design of columns , 1979 .

[17]  Martin P. Bendsøe,et al.  An interpretation for min-max structural design problems including a method for relaxing constraints , 1984 .

[18]  Leonard Spunt,et al.  Optimum structural design , 1971 .

[19]  S. S. Rao,et al.  Literature Review : Optimum Design of Structures Under Shock and Vibration Environment , 1975 .

[20]  William Prager,et al.  Introduction to structural optimization , 1974 .

[21]  James C. Frauenthal Constrained Optimal Design of Columns Against Buckling , 1972 .

[22]  Zenon Mróz,et al.  Optimal Design of Elastic Beams with Unspecified Support Conditions , 1978 .

[23]  Niels Olhoff,et al.  Regularized formulation for optimal design of axisymmetric plates , 1982 .

[24]  C. Wang,et al.  Optimal plastic design of circular plates: numerical solutions and built-in edges , 1986 .

[25]  Zenon Mróz,et al.  Optimal Design of Elastic Structures Subjected to Dynamic, Harmonically‐Varying Loads , 1970 .

[26]  Edward J. Haug,et al.  Optimization of distributed parameter structures , 1981 .

[27]  George I. N. Rozvany,et al.  On the Solid Plate Paradox in Structural Optimization , 1982 .

[28]  Jean-Louis Armand,et al.  Optimal design of bending elements , 1978 .

[29]  E. F. Masur Optimal placement of available sections in structural eigenvalue problems , 1975 .

[30]  L. Icerman,et al.  Optimal structural design for given dynamic deflection , 1969 .

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

[32]  Edward J. Haug,et al.  Problems and methods of optimal structural design , 1983 .

[33]  George I. N. Rozvany,et al.  Optimal plastic design of axisymmetric solid plates with a maximum thickness constraint , 1984 .

[34]  Niels Olhoff,et al.  Optimization of Vibrating Beams with Respect to Higher Order Natural Frequencies , 1976 .

[35]  On the Optimal Shape of an Elastic-Plastic Column , 1976 .

[36]  J. E. Taylor,et al.  Designing Continuous Columns for Minimum Total Cost of Material and Interior Supports , 1978 .

[37]  Bion L. Pierson,et al.  An Optimal Control Approach to Minimum-Weight Vibrating Beam Design , 1977 .

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

[39]  Andrzej Marek Brandt Criteria and Methods of Structural Optimization , 1984 .

[40]  G. Rozvany Analytical Treatment of Some Extended Problems in Structural Optimization, Part I , 1974 .

[41]  M. Kamat,et al.  Strongest Column by the Finite Element Displacement Method , 1972 .

[42]  R. M. Brach,et al.  On the extremal fundamental frequencies of vibrating beams , 1968 .

[43]  Richard H. Gallagher,et al.  Optimum Structural Design: Theory and Applications , 1973 .

[44]  Robert V. Kohn,et al.  A new model for thin plates with rapidly varying thickness , 1984 .

[45]  Jan Błachut,et al.  On unimodal and bimodal optimal design of funicular arches , 1981 .

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

[47]  J. E. Taylor,et al.  On optimal structural remodeling , 1979 .

[48]  Optimal Design of Portal Frames Against Buckling , 1985 .

[49]  J. Keller,et al.  Strongest Columns and Isoperimetric Inequalities for Eigenvalues , 1962 .

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

[51]  David G. Carmichael,et al.  Structural modelling and optimization , 1981 .

[52]  Tomasz Lekszycki,et al.  Optimal Design of Viscoelastic Structures under Forced Steady-State Vibration , 1981 .

[53]  C. Sheu,et al.  Optimal Design of an Elastic Column of Thin-Walled Cross Section , 1968 .

[54]  On the solution of optimization problems with singularities , 1977 .

[55]  J. Keller The shape of the strongest column , 1960 .

[56]  M. Bendsøe,et al.  A Variational Formulation for Multicriteria Structural Optimization , 1983 .

[57]  Alexander P. Seyranian,et al.  Homogeneous functionals and structural optimization problems , 1979 .

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

[59]  V. N. Diyesperov Investigation of selfsimilar solutions describing flows in mixing layers , 1986 .

[60]  Niels Olhoff,et al.  On Structural Optimization , 1983 .

[61]  Sarp Adali,et al.  Optimal shape and non-homogeneity of a non-uniformly compressed column☆ , 1979 .

[62]  N. Olhoff,et al.  On single and bimodal optimum buckling loads of clamped columns , 1977 .

[63]  Antoni Gajewski A note on unimodal and bimodal optimal design of vibrating compressed columns , 1981 .

[64]  R. M. Brach,et al.  On optimal design of vibrating structures , 1973 .

[65]  G. N. Vanderplaats,et al.  Structural Optimization-Past, Present, and Future , 1981 .

[66]  Niels Olhoff,et al.  A method of design against vibration resonance of beams and shafts , 1985 .

[67]  Niels Olhoff,et al.  Designing vibrating beams and rotating shafts for maximum difference between adjacent natural frequencies , 1984 .

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

[69]  Paulo Rizzi,et al.  Optimization of Continuous One-Dimensional Structures under Steady Harmonic Excitation , 1976 .