A unified approach to nonlinear buckling optimization of composite structures

A unified approach to nonlinear buckling fiber angle optimization of laminated composite shell structures is presented. The method includes loss of stability due to bifurcation and limiting behaviour. The optimization formulation is formulated as a mathematical programming problem and solved using gradient-based techniques. Buckling of a well-known cylindrical shell benchmark problem is studied and the solutions found in literature are proved to be incorrect. The nonlinear buckling optimization formulation is benchmarked against the traditional linear buckling optimization formulation through several numerical optimization cases of a composite cylindrical shell panel which clearly illustrates the advantage and potential of the presented approach.

[1]  Brian L. Wardle,et al.  Buckling Response of Transversely Loaded Composite Shells, Part 1: Experiments , 2004 .

[2]  Erik Lund,et al.  Buckling topology optimization of laminated multi-material composite shell structures , 2009 .

[3]  Sarp Adali,et al.  Design of antisymmetric hybrid laminates for maximum buckling load: I. Optimal fibre orientation , 1990 .

[4]  Ekkehard Ramm,et al.  Linear and nonlinear stability analysis of cylindrical shells , 1980 .

[5]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[6]  C. M. Mota Soares,et al.  Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells , 2000 .

[7]  Yoshihiro Narita,et al.  Optimization for the Maximum Buckling Loads of Laminated Composite Plates – Comparison of Various Design Methods , 2007 .

[8]  Johann Arbocz,et al.  Computerized buckling analysis of shells , 1985 .

[9]  Brian L. Wardle,et al.  Buckling Response of Transversly Loaded Composites Shells, Part 2: Numerical Analysis , 2004 .

[10]  E. Riks An incremental approach to the solution of snapping and buckling problems , 1979 .

[11]  G. Sun,et al.  A practical approach to optimal design of laminated cylindrical shells for buckling , 1989 .

[12]  J. M. T. Thompson,et al.  A general theory for the equilibrium and stability of discrete conservative systems , 1969 .

[13]  Kim J.R. Rasmussen,et al.  Nonlinear buckling optimization of composite structures considering ''worst" shape imperfections , 2010 .

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

[15]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[16]  J. S. Hansen,et al.  Optimal Design of Laminated-Composite Circular-Cylindrical Shells Subjected to Combined Loads , 1988 .

[17]  E. Wilson,et al.  An eigensolution strategy for large systems , 1983 .

[18]  N. Olhoff Multicriterion structural optimization via bound formulation and mathematical programming , 1989 .

[19]  Serge Abrate,et al.  Optimal design of laminated plates and shells , 1994 .

[20]  M. Crisfield A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[21]  M. A. Crisfield,et al.  Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics , 1997 .

[22]  Mark Walker,et al.  Multiobjective design of laminated cylindrical shells for maximum torsional and axial buckling loads , 1997 .

[23]  Sven Klinkel,et al.  A continuum based three-dimensional shell element for laminated structures , 1999 .

[24]  Ekkehard Ramm,et al.  Strategies for Tracing the Nonlinear Response Near Limit Points , 1981 .

[25]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[26]  Brian L. Wardle Solution to the Incorrect Benchmark Shell-Buckling Problem , 2008 .

[27]  Sarp Adali,et al.  Design of antisymmetric hybrid laminates for maximum buckling load: II. Optimal layer thickness , 1990 .

[28]  A. B. Sabir,et al.  The applications of finite elements to large deflection geometrically nonlinear behaviour of cylindrical shells , 1972 .

[29]  Hideki Sekine,et al.  Layup Optimization for Buckling of Laminated Composite Shells with Restricted Layer Angles , 2004 .

[30]  Mark A. Tudela,et al.  BUCKLING RESPONSE OF TRANSVERSELY LOADED COMPOSITE SHELLS , 1998 .

[31]  Mark Walker,et al.  Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling , 1996 .

[32]  F. Brogan,et al.  Bifurcation buckling for general shells , 1972 .

[33]  Erik Lund,et al.  Nonlinear Buckling Optimization of Composite Structures , 2010 .

[34]  Niels Olhoff,et al.  Optimization of the buckling load for composite structures taking thermal effects into account , 2001 .

[35]  Aleksander Muc,et al.  Optimal fibre orientation for simply-supported, angle-ply plates under biaxial compression , 1988 .

[36]  Umut Topal,et al.  Multiobjective optimization of laminated composite cylindrical shells for maximum frequency and buckling load , 2009 .

[37]  M. Harnau,et al.  About linear and quadratic Solid-Shell elements at large deformations , 2002 .

[38]  Michael W. Hyer,et al.  Innovative design of composite structures: The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes , 1990 .

[39]  Mark Walker,et al.  Multiobjective design of laminated plates for maximum stability using the finite element method , 2001 .

[40]  Cv Clemens Verhoosel,et al.  Non‐linear Finite Element Analysis , 2012 .

[41]  W. Wunderlich Nonlinear Finite Element Analysis in Structural Mechanics , 1981 .

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

[43]  J. M. T. Thompson,et al.  The Elastic Instability of a Complete Spherical Shell , 1962 .

[44]  Umut Topal,et al.  Maximization of buckling load of laminated composite plates with central circular holes using MFD method , 2008 .

[45]  Hsuan-Teh Hu,et al.  Optimization for buckling resistance of fiber-composite laminate shells with and without cutouts , 1990 .

[46]  J. Grenestedt,et al.  Layup optimization against buckling of shear panels , 1991 .

[47]  Chien-Chang Lin,et al.  Optimum weight design of composite laminated plates , 1991 .

[48]  Erik Lund,et al.  Failure optimization of geometrically linear/nonlinear laminated composite structures using a two-step hierarchical model adaptivity , 2009 .

[49]  Hsuan-Teh Hu,et al.  Buckling optimization of laminated cylindrical panels subjected to axial compressive load , 2007 .

[50]  N. Olhoff,et al.  Multiple eigenvalues in structural optimization problems , 1994 .

[51]  C. M. Mota Soares,et al.  Buckling sensitivity analysis and optimal design of thin laminated structures , 1997 .

[52]  Carlos Alberto Brebbia,et al.  Variational Methods in Engineering , 1985 .

[53]  Brian Wardle The Incorrect Benchmark Shell Buckling Solution , 2006 .

[54]  Hisao Fukunaga,et al.  Buckling design of symmetrically laminated plates using lamination parameters , 1995 .

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

[56]  Robert M. Jones,et al.  Buckling of Bars, Plates and Shells , 2007 .