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Combined shape and non-shape sensitivity for optical design of metal forming operations

Antunez H., Kowalczyk M.

Computer Assisted Mechanics and Engineering Sciences

2004

Vol. 11, No. 1

99-118

Shape and non-shape optimization is carried out for metal forming processes. This means a unified treatment of both shape parameters and other process parameters which are assumed to be design variables. An optimization algorithm makes use of the results of the analysis problem and of the sensitivity parameters obtained as a byproduct of the basic solution, in the context of the direct differentiation method. The shape sensitivity stage is formulated within the domain parametrization approach. Two alternative mappings are proposed to obtain the required derivatives with respect to the shape parameters. The behaviour of different functionals considered and the effect of the boundary conditions on the optimal design are discussed.

Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials

Dłużewski P., Jurczak G., Antunez H.

Computer Assisted Mechanics and Engineering Sciences

2003

Vol. 10, No. 1

69-79

A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative - instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models.