Mathematical programming in engineering mechanics: some current problems

The application of mathematical programming methods in a variety of practically motivated engineering mechanics problems provides a fertile field for interdisciplinary interaction between the mathematical programming and engineering communities. This paper briefly outlines several topical problems in engineering mechanics involving the use of mathematical programming techniques. The intention is to attract the attention of mathematical programming experts to some of the still open questions in the intersection of the two fields.

[1]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[2]  Gautam Mitra,et al.  An enumerative method for the solution of linear complementarity problems , 1988 .

[3]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[4]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[5]  Giulio Maier,et al.  Generalized variable finite element modeling and extremum theorems in stepwise holonomic elastoplasticity with internal variables , 1992 .

[6]  Giulio Maier,et al.  Static shakedown theorems in piecewise linearized poroplasticity , 1998 .

[7]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[8]  Christian Kanzow,et al.  Some Noninterior Continuation Methods for Linear Complementarity Problems , 1996, SIAM J. Matrix Anal. Appl..

[9]  Ming-Wan Lu,et al.  An algorithm for plastic limit analysis , 1995 .

[10]  Giulio Maier,et al.  Parameter Identification of the Cohesive Crack Model , 1997 .

[11]  Yiu-Wing Mai,et al.  Advances in Fracture Research , 1997 .

[12]  Giulio Maier,et al.  Indirect identification of yield limits by mathematical programming , 1982 .

[13]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..

[14]  Alberto Corigliano,et al.  Dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative, internal variable constitutive laws , 1995 .

[15]  Antonio Capsoni,et al.  A FINITE ELEMENT FORMULATION OF THE RIGID–PLASTIC LIMIT ANALYSIS PROBLEM , 1997 .

[16]  Giulio Maier,et al.  Some aspects of quasi-brittle fracture analysis as a linear complementarity problem , 1994 .

[17]  Daniel Ralph,et al.  Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints , 1999, SIAM J. Optim..

[18]  C. W. J. Oomens,et al.  Material Identification Using Mixed Numerical Experimental Methods , 1997 .

[19]  Francisco Facchinei,et al.  A smoothing method for mathematical programs with equilibrium constraints , 1999, Math. Program..

[20]  Michael C. Ferris,et al.  Nonlinear programming approach for a class of inverse problems in elastoplasticity , 1998 .

[21]  Michael C. Ferris,et al.  Complementarity and variational problems : state of the art , 1997 .

[22]  Z. Bažant FRACTURE MECHANICS OF CONCRETE STRUCTURES , 1992 .

[23]  Giulio Maier Inverse problem in engineering plasticity: a quadratic programming approach , 1981 .

[24]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[25]  Aurelio Muttoni,et al.  Fracture and Damage in Quasibrittle Structures , 1994 .

[26]  G. Maier,et al.  On multiplicity of solutions in quasi-brittle fracture computations , 1997 .

[27]  S. Dirkse,et al.  The path solver: a nommonotone stabilization scheme for mixed complementarity problems , 1995 .

[28]  A. Nappi System identification for yield limits and hardening moduli in discrete elastic-plastic structures by nonlinear programming , 1982 .

[29]  M. Ferris,et al.  Complementarity problems in GAMS and the PATH solver 1 This material is based on research supported , 2000 .

[30]  Ikuyo Kaneko On some recent engineering applications of complementarity problems , 1982 .

[31]  Bernhard A. Schrefler,et al.  The Finite Element Method in the Deformation and Consolidation of Porous Media , 1987 .

[32]  Gabriella Bolzon,et al.  Hybrid finite element approach to quasi-brittle fracture , 1996 .

[33]  G. Maier,et al.  Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems , 1993, Computational Mechanics.

[34]  M. Z. Cohn,et al.  Engineering Plasticity by Mathematical Programming , 1981 .

[35]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[36]  Giulio Maier,et al.  BIFURCATIONS AND INSTABILITIES IN FRACTURE OF COHESIVE-SOFTENING STRUCTURES: A BOUNDARY ELEMENT ANALYSIS† , 1992 .

[37]  G. Maier A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .