SUMMARYIn this work a homogenization method is presented to obtain by numerical simulation interface laws for normal contact pressure based on statistical surface models. For this purpose and assuming elastic behaviour of the asperities, the interface law of Kragelsky et al. (Friction and Wear-Calculation Methods, Pergamon, 1982) is chosen for comparison. The non-penetration condition and interface models for contact that take into account the surface micro-structure are investigated in detail. A theoretical basis for the three-dimensional contact problem with ÿnite deformations is shortly presented. The augmented Lagrangian method is then used to solve the contact problem with friction. The algorithms for frictional contact are derived based on a slip rule using backward Euler integration like in plasticity. Special attention was dedicated to the consistent derivation of the contact equations between ÿnite element surfaces. A matrix formulation for a node-to-surface contact element is derived consisting of a master surface segment with four nodes and a contacting slave node. It was also necessary to consider the special cases of node-to-edge contact and node-to-node contact in order to achieve the desired asymptotic quadratic convergence in the Newton method. A numerical example is selected to show the ability of the contact formulation and the algorithm to represent interface law for rough surfaces.
In this work, the non-penetration condition and the interface models for contact, taking into account the surface microstructure, are investigated in detail. It is done using a homogenization procedures presented by Bandeira, Wriggers and Pimenta (2001a), to obtain by numerical simulation the interface behavior for the normal and tangential contact pressures, based on statistical surface models. The contact surfaces of both bodies are rough. This paper can be regarded as a complementary study to that presented by Bandeira, Wriggers and Pimenta (2006). Here, the plasticity of the asperities is taken into account by assuming a constitutive equation based on an associated von Mises yield function formulated in principal axes. The plastic zones in the microstructure are shown to study in detail the contact interface. Numerical examples are selected to show the ability of the algorithm to represent interface law for rough surfaces, considering elastoplastic behaviour of the asperities.
The basic aim of this work is to compile the theoretical basis of ACI 440.2R: 2008 [1] with the NBR 6118: 2014 [2] in order to take into account the concepts of the Brazilian standard in flexural sizing of reinforced beams with CFRP (Carbon Fiber Reinforced Polymer). The contribution of the Brazilian standard is given particularly with regard to the application of its safety coefficients and material properties (steel and concrete), including its deformation limits. For this purpose, a beam is adopted as a reference for the study, where two reinforcement designs are performed with CFRP, one from the compiled formulations and another considering only the requirements of ACI 440.2R: 2008 [1]. The results obtained are compared below. Finally, through the ANSYS software, numerical modeling of the reference beam is carried out, where tensions and deformations presented by concrete, steel and carbon fiber are observed. The results of the numerical analysis are compared with those obtained from the formulations compiled in order to validate the numerical model adopted in this study. The research concludes that in flexural sizing the areas of PRFC dimensioned from the formulations of ACI 440.2R: 2008 [1] resulted in values very close to those obtained by the formulations compiled. In addition, it was concluded that the numerical modeling performed in this work represented well the behavior of the structure, because the rupture loads were approximately equal to those expected by the analytical formulations.
Este trabalho tem como objetivo apresentar métodos implícitos de otimização aplicados à engenharia de estruturas. São apresentados de forma sucinta os Método de Newton, Método do Lagrangiano, Método da Penalidade e Método do Lagrangiano Aumentado. É apresentada uma base teórica sobre os conceitos e os algoritmos de programação matemática para cada um destes métodos e posteriormente, são apresentados exemplos de aplicação utilizando os métodos estudados. Estes métodos são amplamente utilizados nos programas de elementos finitos para a análise de estruturas. Este artigo não tem objetivo de apresentar o Método dos Elementos Finitos, mas sim, apresentar alguns exemplos de modelagem estrutural utilizando este método. É imprescindível ressaltar a importância do conhecimento destas ferramentas no processo de análise de estruturas quando se utiliza a modelagem em elementos finitos.
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