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5.PotentialEnergy

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    Prof. Gian Paolo Cimellaro & Prof. Giuseppe Marano Dipartimento d’ingegneria strutturale e geotecnica, Politecnico di Torino  Automatic Calculus Lec 5 Principles of minimum potential energy and Rayleigh-Ritz-Galerkin  Summary: ã Exact solution ã Potential energy of a system ã Elastic bar ã Principle of Minimum Potential Energy ã Rayleigh-Ritz-Galerkin Principle  A generic 1D problem Solution strategy : 1. Exact solution  (Closed-form solution) 2. Approximate solutions 2.1 Variational Method   (Minimum of Total Potential Energy) 2.2 Weigthed Residual Methods  (Galerkin method)   11 11 ( ) ( ) ... ( ) ( ) n nn nn n d x d x dxc x c x c x f xdt dt dt           A generic problem 22 ( ) ( ) d u E A x b xdx     EXACT SOLUTION
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