Wellington Andrade Da Silva

Uma abordagem analítica para detecção de pontos limites e de bifurcação

RESUMO: Neste trabalho descreve-se analiticamente de maneira detalhada a deteccao e a classificacao de pontos criticos na trajetoria primaria de equilibrio de sistemas estruturais. Utiliza-se a Formulacao Lagrangiana Total para descrever a cinematica de um elemento de barra biarticulado 2D. Atraves desta formulacao obtem-se o vetor de forcas internas e a matriz de rigidez tangente que levam em conta os efeitos da nao linearidade geometrica. Assume-se um modelo constitutivo linear elastico para o estado uniaxial de tensao-deformacao, usando a deformacao de Green-Lagrange e a tensao axial do segundo tensor de Piola-Kirchhoff que sao energeticamente conjugados. Como estudo de caso apresenta-se uma trelica plana hiperestatica composta com 3 elementos biarticulados 2D e com dois graus de liberdade. Por fim, determinam-se as condicoes geometricas e fisicas para a coalescencia entre os pontos limites e de bifurcacao. A principal contribuicao deste trabalho e demonstrar a necessidade de compreender melhor os fenomenos nao lineares para projetar sistemas estruturais mais seguros. ABSTRACT: Using an analytical this paper describes in detail the detection and classification of critical points in the primary equilibrium path of structural systems. The Total Lagrangian formulation is employed to describe the kinematics of a 2D bar element. With this formulation, the internal force vector and the tangent stiffness matrix including the geometric nonlinearity effects are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. Such model uses the Green-Lagrange strain tensor and the second Piola-Kirchhoff axial stress tensor which are energetically conjugate tensors. As a study case, the article presents a statically inderminate plane truss discretized with three 2D bar elements. Finally, the geometrical and physical conditions for the coalescence between limit and bifurcation points are determined. The main contribution of this work is to demonstrate the need to better understanding the non linear phenomena. Such understanding is necessary for designing safer structural systems.

ANÁLISE NUMÉRICA DE BLOCOS SOBRE DUAS ESTACAS COM CÁLICE EMBUTIDO SUBMETIDO À AÇÃO DE FORÇA HORIZONTAL

The structural behavior of pile caps with sockets embedded is influenced by interface of column-socket, which can be smooth or rough. With intent to analyzer the behavior of two pile caps with embedded socket, considering the friction between the column and the socket, subjected to horizontal force, the numerical simulations were carried out, using a program based on the Finite Element Methods (FEM). In the numerical analysis the non-linear behavior of materials was considered, also the friction between the column and the socket. It was considered perfect bond between the reinforcement and the concrete around. It was observed that the embedded length is preponderant factor in the structural behavior of the analyzed element. Keywords: foundations, pile caps, numerical analysis.