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The present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is difficult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational efficiency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with sufficient accuracy for shape optimization applications. Copyright © 2002 John Wiley & Sons, Ltd.

PARENTE JUNIOR, E. ; VAZ, L. E. Improvement of semi-analytical design sensitivities of non-linear structures using equilibrium relations. International Journal for Numerical Methods in Engineering, v. 50, n.9, p. 2127-2142, 2001.

This work presents a finite element implementation to treat the Hydromechanical Coupling (HM) in fractured rock masses under the framework of the so-called ‘equivalent continuum’ approach. The multilaminar concept, introduced by Zienkiewicz and Pande, is used to simulate the mechanical behaviour of both the intact rock and the families of fractures. In that concept, the non-linearities in the constitutive relations are dealt by means of fictitious viscoplasticity. In the present implementation, the mechanical behaviour of the fractures is modelled by means of Barton–Bandis model. The shear stress/shear displacement/dilatancy relationship is modelled as viscoplastic and the normal stress/normal displacement as non-linear viscoelastic. Flow along fractures is considered to occur as a sequence of permanent states. The permeability tensor of the equivalent continuum is determined from the hydraulic apertures, in accordance of Barton et al. From the numerical point of view, the basic aim of the work is the implementation of an efficient scheme to solve the above described problem. This is done by designing a self-adaptive time step control, transparent to the user, which determines the highest possible time step while assuming the conditions of precision, stability and convergence. The paper presents the numerical details of such scheme together with validation/comparative examples and the results obtained on the analysis of the fractured rock foundation of a hypothetical dam. © 1998 John Wiley & Sons, Ltd.

A new approach for performing FE-shape design sensitivity analyses (DSA) of structural models with both linear elastic and elastoplastic material behaviour is presented. In the formulation of the method the derivation of the FE equilibrium equations is performed analytically leading to various terms. The differentiation of some parts of these terms is determined numerically, therefore the method is semianalytical. The formulation is particularized for isoparametric finite elements for which “exact” numerical differentiation can be obtained (exact up to round-off error). Examples of some plane stress problems testify that the results of the new method are not dependent either on the size of perturbation of the design variables or on the FE mesh refinement among other factors.