Humberto Breves Coda

Two-dimensional solids reinforced by thin bars using the boundary element method

In this work, a linear boundary element formulation is presented for analyzing stiffened domains. A particular sub-region technique, in which the equilibrium is preserved along interfaces without traction approximation, is adapted to model fiber immersed in a body. The integral representation is written for a whole body, requiring only the displacement along interfaces. The sub-region is then assumed to be very thin to simulate fibers only when normal forces are taken into account. The thin sub-regions then degenerate so that they can be represented by its skeleton line. The displacement field over the fiber cross-sections is assumed to be constant. In the case of 2D problems, the degrees of freedom are reduced to two components only at each fiber node. Thus, displacement integral representations for collocations defined along the fiber skeleton are needed. The quasi-singular integrals are computed by using closed expressions or employing a numerical scheme with sub-elements. An example is solved to show that the formulation is very accurate for modeling cases of domains stiffened by fibers.

Dynamic and static non-linear analysis of reinforced media: a BEM/FEM coupling approach

Abstract This work is concerned to the development and application of an effective boundary element/finite element coupling to analyse the static and dynamic behaviours of reinforced media, as for example, reinforced concrete or reinforced polymers. The boundary element formulation is based on the mass matrix approach and the finite element formulation is developed to make easier the non-linear coupling. Particularly, the finite elements are considered as simple truss elements with longitudinal unknown distributed forces that provide the contact between the internal fibres and the matrix material. The non-linear influences of the finite elements are considered as residual forces imposed on the boundary element non-linear system of equation. An internal line force is created inside the boundary element domain, in order to make possible the coupling. Experimental static results are used to validate the developed theory. Dynamic results obtained with other numerical techniques are taken in order to validate the general formulation.

On the coupling of 3D bem and fem frame model applied to elastodynamic analysis

This work presents the coupling of framed structures approached by finite elements with three-dimensional bodies represented by the boundary element method. The coupling is particularly dedicated to analyse three-dimensional half space stiffened by piles and other composite domain problems, for which static and dynamic cases have been taken into account. Some numerical examples are analysed to point out the power and the accuracy of the proposed scheme.

Dynamic non-linear stress analysis by the mass matrix BEM

This paper deals with the elastoplastic boundary element formulation applied to transient problems. An improved procedure to take into account the non-linear influences on acceleration and velocity is proposed. Integral representations of displacements and strains are derived taking into account the following domain terms: plastic strains, mass effects, viscosity and other temperature-like effects. The required domain variable approximations are given by adopting internal cells over which shape functions are properly defined. The Kelvin static fundamental solution is used in writing the integral representations, which gives the matrix time dependent differential equation that governs the problem.

Three-dimensional transient BEM analysis

In this work the three-dimensional transient boundary element method (BEM) is studied to show its applicability when solving several problems in engineering. A general technique to combine the BEM with the finite element method (FEM) is presented, with particular emphasis on studying building structures interacting with their foundations. In order to improve the stability of the developed numerical algorithm, a modified time dependent fundamental solution was derived. The article also shows a numerical scheme to deal with time singular integrals over flat triangular and quadrangular elements.

A simple comparison between two 3D time domain elastodynamic boundary element formulations

The three-dimensional transient boundary element method for elastodynamic analysis is studied here to verify its performance concerning some required features when solving practical problems. The classical formulation was established more than 10 years ago and has already been applied several times, mainly in the context of infinite domain analysis. In this work the classical fundamental solution is compared with an alternative one in which a fundamental solution based on the unit impulse is assumed distributed over a time interval. Some interesting aspects of both solutions, regarding the result confidence for practical analysis, are also discussed in the paper.

Physical and geometrical non-linear analysis of plane frames considering elastoplastic semi-rigid connections by the positional FEM

This study presents an alternative Finite Element formulation based on positions to model plane frames considering geometrical non-linear and elastoplastic behavior for members and semi-rigid connections. The formulation includes shear effects and allows the consideration of important mechanical behavior of structures in design decisions and verifications. The principle of stationary energy is used to find the equilibrium equations. A multi-linear elastoplastic constitutive law is developed for both continuum members and semi-rigid connections in order to comprise any proposed stress-strain diagram. Large rotations and displacements are considered for both semi-rigid connections and structure. The most important steps used to derive the formulation are described along the paper and various examples are used to validate and show the possibilities of the proposed technique.

Non-singular time-stepping BEM for transient elastodynamic analysis

In this work a general boundary element formulation for transient elastodynamic analysis employing outside collocation points is developed. Before introducing the formulation, a discussion on the physical meaning of the boundary integral representations for time domain elastodynamic BEM is presented. The way to perform time translations of elastodynamic states is shown. The advantage of this procedure is given by the possibility of avoiding either the direct or indirect evaluation of singular integrals over the elements that contain the source points, as well as by computing corner free terms required for continuous discretizations of solids with complex geometry.

A shell finite element formulation to analyze highly deformable rubber-like materials

Abstract: In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubber-like materials is presented. The element is a triangular shell of any-order with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the Reissner-Mindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cooks membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking.

Material and geometric nonlinear analysis of reinforced concrete frame structures considering the influence of shear strength complementary mechanisms

A mechanical model for the analysis of reinforced concrete frame structures based on the Finite Element Method (FEM) is proposed in this paper. The nonlinear behavior of the steel and concrete is modeled by plasticity and damage models, respectively. In addition, geometric nonlinearity is considered by an updated lagrangian description, which allows writing the structure equilibrium in the last balanced configuration. To improve the modeling of the shear influence, concrete strength complementary mechanisms, such as aggregate interlock and dowel action are taken into account. A simplified model to compute the shear reinforcement contribution is also proposed. The main advantage of such a model is that it incorporates all these effects in a one-dimensional finite element formulation. Two tests were performed to compare the provided numerical solutions with experimental results and other one- and bi-dimensional numerical approaches. The tests have shown a good agreement between the proposed model and experimental results, especially when the shear complementary mechanisms are considered. All the numerical applications were performed considering monotonic loading.