Structural optimisation of axisymmetric and prismatic shells and folded plates

Abstract This paper deals with the development and application of reliable, creative and efficient computational tools for the structural optimisation of variable thickness axisymmetric and prismatic shells and folded plates using computer-aided analysis and design procedure. The problem of finding optimal forms and thickness variations for such structures is solved by integrating computer aided geometry modelling tools, automatic mesh generation, structural analysis, sensitivity evaluation and mathematical programming methods. The shape and thickness variation of the structures are defined using parametric cubic splines and the structural analysis is carried out with either finite element or finite strip methods in which Mindlin-Reissner assumptions are adopted. In static situations, the composition of the strain energy is monitored during the optimisation process to obtain insight into the energy distribution for the optimum structures. This allows us to demonstrate that, in the majority of cases, the optimum shells are membrane energy dominated as might be expected. For the vibrating structures, the mode shapes of the initial and optimum solutions are presented. A set of carefully defined, unambiguous benchmark examples is presented and studied with independent verification to test the various features of the structural optimisation process.

[1]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[2]  Mustafa Özakça,et al.  Optimum Shapes Of Vibrating Axisymmetric Plates And Shells , 1993 .

[3]  Mark S. Shephard,et al.  Approaches to the Automatic Generation and Control of Finite Element Meshes , 1988 .

[4]  J. L. Marcelin,et al.  OPTIMAL SHAPE DESIGN OF THIN AXISYMMETRIC SHELLS , 1988 .

[5]  K. S. Lo,et al.  Computer analysis in cylindrical shells , 1964 .

[6]  Mustafa Özakça,et al.  Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells: Part 2: shape optimization , 1995 .

[7]  E. Hinton,et al.  Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 2: Shape optimisation , 1993 .

[8]  O. C. Zienkiewicz,et al.  A simple and efficient element for axisymmetric shells , 1977 .

[9]  B. H. V. Topping,et al.  Shape Optimization of Skeletal Structures: A Review , 1983 .

[10]  Yunliang Ding,et al.  Shape optimization of structures: a literature survey , 1986 .

[11]  E. Hinton,et al.  Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 1: Finite strip formulation , 1993 .

[12]  David M. Potts,et al.  CURVED MINDLIN BEAM AND AXI-SYMMETRIC SHELL ELEMENTS : A NEW APPROACH , 1990 .

[13]  Raphael T. Haftka,et al.  Recent developments in structural sensitivity analysis , 1989 .

[14]  B. Su,et al.  Computational geometry: curve and surface modeling , 1989 .

[15]  Mo Shing Cheung,et al.  Free Vibration of Curved and Straight Beam Slab or Box Girder Bridges , 1972 .

[16]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .

[17]  T. Charnley,et al.  Normal modes of the modern English church bell , 1983 .

[18]  D. Owen,et al.  Finite element software for plates and shells , 1984 .

[19]  Phillip L. Gould,et al.  Finite Element Analysis of Shells of Revolution , 1985 .

[20]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .