ME 570: Nonlinear Solid Mech Design

Class Description:

Optimality conditions; finite element methods; design sensitivity analysis; nonlinear analysis; transient analysis; thermo-mechanical solid mechanics. Prerequisite: One of AE 420, CEE 470, ME 471, TAM 470; TAM 445, TAM 551.

Daniel Tortorelli, Solid Mechanics: Analysis and Design with the Finite Element Method (class notes).

Other recommended books:

R. M. Bowen, Introduction to Continuum Mechanics for Engineers, Plenum Press, 1989.
P.Chadwick, Continuum Mechanics: Concise Theory and Problems, Dover Publications, Inc., Mineola, New York.
J. Bonet and R.D. Wood, Nonlinear continuum mechanics for finite element analysis, Cambridge University Press, Cambridge UK, 1997.
M. A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials, John Wiley and Sons, New York, 1991.
R. Fletcher, Practical Methods of Optimization, second edition, John Wiley & Sons, New York, 1987.
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, New York, Academic Press, 1981.
R. T. Haftka and Z. Gurdal, Elements of Structural Optimization (Revised), Kluwer Academic, 1992.
E. J. Haug, K. K. Choi, and V. Komkov, Design Sensitivity Analysis of Structural Sys- tems, volume 177 of Mathematics in Science and Engineering, Academic Press, Orlando, FL, 1986.


Introduction (14 hours)
Mathematical preliminaries. Nonlinear programming: optimality conditions, and optimization algorithms. Nonlinear programming applications: design optimization, inverse / identification analysis, and reliability study.

Linear finite element analyses (4 hours)
1-D spring models, finite element analysis, design sensitivity analysis, and optimization application.

One-dimensional elasticity (10 hours)
Governing equation derivation, design sensitivity analyses with respect to non-shape parameters, shape sensitivity analysis, and variational methods.

Three dimensional linear elastostatics (20 hours)
Governing equation derivation, design sensitivity analysis, finite element analysis, and topology optimization.

Three dimensional nonlinear elastodynamics (12 hours)
Newton-Raphson iteration, Newmark’s method, governing equation derivation, design sensitivity analysis, and finite element analysis.


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