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The direct deformation problem
The sensitivity deformation problem
Metal forming design
6 other sections not shown
algorithm B-bar Bezier curve boundary constitutive equations constraints contact and friction contact tractions corresponding Coulomb friction current forming stage DDM and FDM defined deformation gradient deformed configuration design derivatives design sensitivities design variables developed deviatoric direct contact problem direct deformation problem equivalent stress Example 3.3 F-bar method FDM sensitivity computations final product finite element finite element analysis free surface frictionless geometry grid increment Initial and deformed initial configuration isolated triangles isotropic kinematic large deformation linear material point mesh metal forming processes Newton-Raphson iteration node normal and tangential objective function obtained optimal preforms parameter sensitivity perturbed plastic deformation plastic strain preform design quadrilateral reference configuration remeshing operations Schematic sensitivity analysis sensitivity contact problem sensitivity deformation problem sensitivity formulation shape sensitivity problem shear modulus shown in Figure simulation solution scheme spatial variation temperature thermal tn+i transfer operator updated Lagrangian vector void fraction workpiece