Alguns desenvolvimentos do metodo dos elementos de contorno aplicado a placas semi-espessas

Dissertação (mestrado) - Universidade de Federal de Santa Catarina, Centro TecnologicoO método dos elementos de contorno é aplicado a problemas de placas modeladas pelas teorias de Windlin Ereissner. São resolvidos problemas de flexão linear elástica e estabilidade. vários procedimentos de integração para integrais singulares são testados

Constitutive framework of a new hyperelastic model for isotropic rubber-like materials for finite element implementation

The strain energy function of hyperelastic material models must fulfill some mathematical conditions to satisfy requirements such as numerical stability and physically plausible mechanical behavior. In the framework of computer simulations with Newton-type methods, numerical stability is assured by the positive definiteness of the tangent operator. The Baker-Ericksen inequalities, on the other hand, are sufficient and necessary conditions in order to guarantee that the material behaves in a physically plausible way, although they are rarely taken into account during parameter identification. The present work proposes a modification in the strain energy function of a previously developed model for isotropic rubber-like materials. The new expression for W allows the satisfaction of both of the aforementioned requirements. The complete constitutive framework for its implementation in a Finite Element code is provided. Representative examples are analyzed and to show the superior performance when compared to well-known models found in the specialized literature both for homogeneous and non-homogeneous cases of deformation

Sensitivity analysis of 3D frictional contact with BEM using complex-step differentiation

This paper presents a study of the complex step differentiation method applied to a parameter sensitivity analysis for 3D elastic contact problem. The analysis is performed with the Boundary Element Method (BEM) using discontinuous elements and the Generalized Newton Method with line search (GNMls). A standard BEM implementation is used and the contact restrictions are fulfilled through the augmented Lagrangian method. This methodology in conjunction with the BEM avoids the calculation of the nonlinear derivatives during the solution process, allowing a fast and reliable solution procedure. The parameter sensitivity is evaluated using complex-step differentiation. This well-known method approximates the derivative of a function analogously to the standard finite differences method, with the advantages of being numerically exact and nearly insensitive to the step-size. As an example, a Hertz-type problem is solved and the sensitivity of the contact pressures with respect to the Young Modulus variation is evaluated. The obtained results are compared with analytical and numerical solutions found in the literature

Análise de cargas de flambagem em latas de tinta padrão

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A recursive methodology to determine the mechanical Response of thin laminated plates in bending

The paper’s objective is to present the development of a recursive methodology which is based on Adomian Decompostion Method in order to evaluate the mechanical response of thin laminated plates in linear bending. By the equivalent layer concept, the linear relation between the equivalent stresses and the strains, namely ABD matrix, is established. When viewed by the Adomian Decompostion Method perspective, it generates an interesting idea: each layer influence on the plate’s response can be recursively inserted into a base solution by a rearrangement of the plate’s properties. This base solution is previously obtained and it is, in this paper, an isotropic plate response for the same loading and boundary conditions. This approach can significantly increase optimization and delamination studies, given the simplicity on the layers modification, both in fiber orientation and constitutive properties, as these are considered on the recursive procedure. The pb-2 Rayleigh-Ritz Method is used to approximate the solution space and to generate analytic response surfaces. The methodology is applied to symmetrical and unsymmetrical stacking cases for different boundary conditions sets and loading types and the obtained responses are compared to those found on the literature. A study of case complements the methodology analysis: a simplified landing gear door is modeled considering a set of loading conditions as well as different stacking configurations. Good correspondence was found in all studied cases