Finite Element and Numerical Methods with Integrable / Differentiable Objects.
      
      

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Finite Element Method (source files under directory "fe/")
Preliminary : 2nd-order & 4th-order, Nonlinear ODEs / Transient / Matrix Substructuring
(1-D Elements: Linear Line, Quadratic Line, Axisymmetrical cylindrical. Formulations: Irreducible, Mixed, Lagrangian multiplier, Penalty Function, Galerkin, Least Squares)
Primer: Heat Conduction / Potential Flow / Elasticity / Stokes Flow / Plate Bending
(2-D Elements: Triangular, bilinear, 4-to-9 nodes Lagragian, Formulations: B-Matrix (strain-displacement matrix), Indicial Notation (in l-m), Coordinat-Free Tensorial Notation, Post-processing: Nodal Reaction, Stress & Strain on both Gauss Point and Nodal Projection, Selective Reduced Integrations: Shear-Locking & Dilatation-Locking, Patch Test: Consistency, Stability, Weak, Higher-Order, and  Conforming/Non-conforming Elements)
Advanced: Mixed & Hybrid Methods / Contact Mechanics / Finite Elastoplastic Deformation
(Mixed Methods: Helliger-Reissner / Hu-Washizu Variational Principles, Incompressible u-p & Incompressible u-p-e_v Formulations, B Formulations, Hourglass Elements, Hybrid Methods: Irreducible Subdomain, Pian-Sumihara Element, Reissner-Mindlin Plate Theory: q-w irreducible and q-S-w Mixed Formulations, Contact Mechanics: Mixed Formulation, Contact Searching Algorithm, Elastoplasticity: Incremental Loading alogrithm, Radial Return Mapping alogrithm, Finite Deformation: Finite Stress-Strain Measures, Multiplicative Elastoplastic Decomposition, Covariant Algorithm)

Begin Downloading Finite Element Methods application examples  (fe.exe; 225 KB self-extracting zip file).

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