Andréa Regina Dias da Silva

Numerical methods for analysis of plates on tensionless elastic foundations

Abstract A numerical methodology for analysis of plates resting on tensionless elastic foundations, described either by the Winkler model or as an elastic half-space, is presented in this paper. The contact surface is assumed unbonded and frictionless. The finite element method is used to discretize the plate and foundation. To overcome the difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the frictionless unilateral contact condition, a variational formulation equivalent to these equations is presented from which three alternative linear complementary problems (LCP) are derived and solved by Lemke’s complementary pivoting algorithm. In the first formulation, the LCP variables are the plate displacements and the elastic foundation reaction, in the second, the LCP is derived in terms of the elastic foundation reaction and, in the third formulation, the variables are the elastic foundation displacements and the gap between the bodies. Once the LCP is solved the no-contact regions where the plate lifts up away from the foundation and the sub-grade reaction, as well as the plate displacements and stresses, can be easily obtained. The methodology is illustrated by three examples and the results are compared with existing analytical and numerical results found in the literature.

Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation

The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.

Iterative strategies associated with the normal flow technique on the nonlinear analysis of structural arches

A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with static nonlinear behavior is based on the Newton-Raphson iterative scheme to which are coupled the path-following methods. In this context, this study uses one technique, referred to as normal flow, in the process of obtaining the approximate nonlinear static response of struc tural systems. Basically, this technique is an adaptation made with in the NewtonRaphson iterative scheme in an attempt to speed up the nonlinear solution process and/or remove convergence problems. To overcome the critical points and to trace the whole nonlinear equilibrium path, three different strategies are used in association with the normal flow technique: the cylindrical arc-length, the minimum residual dis placement norm and the generalized displacement. With this procedure, the performance of these strategies when associated with the normal flow technique is valued. Two arches with highly nonlinear load-displacement curves are used in the study. The results obtained demonstrated that the association of the generalized displacement strategy with the normal flow technique contributes to the improvement of the non linear solution methodology.

Aplicação de um elemento finito híbrido não linear na modelagem de estruturas metálicas

In this work, a hybrid finite element that incorporates in its formulation the second-order effect, material yielding and connection flexibility effects are presented to study the behavior of plane steel frames. In fact, it is the classic beam-column finite element that presents, at its ends, pairs of springs arranged in sequence. One of the springs is represented in the mathematical formulation of this element by the parameter Sc, which defines the joint stiffness of the members; the other spring, whose rigidity is simulated by the parameter Ss, evaluates the plastification of the cross section. The element stiffness matrix incorporates these three mentioned nonlinear effects. Therefore, the aim of this work is to investigate the computer efficiency of this hybrid finite element in the isolated and combined simulation of these nonlinear effects. Initially, equilibrium and stability of classic structural problems with high nonlinear behavior and critical points in the equilibrium paths are studied. Semi-rigid structural systems with initial geometric imperfections are also evaluated. Later, the hybrid element is tested in the inelastic analysis of plane steel frames based on refined plastic-hinge method. Through these examples, it was possible to validate and verify the use of the proposed hybrid finite element in the numerical modeling of various nonlinear structural problems in civil engineering.