Abstract

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timet u (t u<t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.

For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some example

Abstract

Nowadays, the finite element analyses provide beneficial support in many fields of engineering by means of their cost, time and capacity saving characteristics. During the analyses, the one of the key elements is the correctly defined material properties. This is especially true for the plastics due to their orthotropic and nonlinear material properties as plasticity, relaxation or creep for example. Additionally, the applications of the plastics are widely spread in the automotive engineering beside the other sectors of the industry. Hence, the main goal of the present research is to verify static structural and to validate impact dynamic simulation results by the available material data and actually performed measurement results respectively. Tensile test and creep simulations were carried out in Ansys Workbench software for comparing the static structural simulation results with the available material data given by the material manufacturer in case of the used test samples, boundary conditions and material properties. Following the verification, the material models were applied for a specimen and for a model of an existing product in order to complete validation of the explicit dynamic simulation’s results. Real vertical hammer tests were set up and performed for this purpose and the same procedure was simulated also in order to be able to compare the results and drawn conclusions about the accuracy of the calculation method.