A hybrid-Trefftz formulation for plane elasticity with selective enrichment of the approximations

This work is related to the so-called non-conventional finite element formulations. Essentially, a methodology for the enrichment of the initial approximation which is typical of the meshless methods and based on the clouds concept is introduced in the hybrid-Trefftz formulation for plane elasticity. The formulation presented allows for the approximation and direct enrichment of two independent fields: stresses in the domains and displacements on the boundaries of the elements. Defined by a set of elements and interior boundaries sharing a common node, the cloud notion is employed to select the enrichment support for the approximation fields. The numerical analysis performed reveals an excellent performance of the resulting formulation, characterized by the good approximation ability and a reduced computational effort. Copyright (C) 2009 John Wiley & Sons, Ltd.

Proposal of a test specimen to evaluate the shear strength of vertical interfaces of running bond masonry walls

There is no normalized test to assess the shear strength of vertical interfaces of interconnected masonry walls. The approach used to evaluate this strength is normally indirect and often unreliable. The aim of this study is to propose a new test specimen to eliminate this deficiency. The main features of the proposed specimen are failure caused by shear stress on the vertical interface and a small number of units (blocks). The paper presents a numerical analysis based on the finite element method, with the purpose of showing the theoretical performance of the designed specimen, in terms of its geometry, boundary conditions, and loading scheme, and describes an experimental program using the specimen built with full- and third-scale clay blocks. The main conclusions are that the proposed specimen is easy to build and is appropriate to evaluate the sheaf strength of vertical interfaces of masonry walls.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

Mechanical strength evaluation for Nd-YAG laser and electric resistance spot weld (ERSW) joint under multiaxial loading

This work presents a comparison between laser weld (LBW) and electric resistance spot weld (ERSW) processes used for assemblies of components in a body-in-white (BIW) at a world class automotive industry. It is carried out by evaluating the mechanical strength modeled both by experimental and numerical methods. An ""Arcan"" multiaxial test was designed and manufactured in order to enable 0 degrees, 45 degrees and 90 degrees directional loadings. The welded specimens were uncoated low carbon steel sheets (S-y = 170 MPa) used currently at the automotive industry, with two different thicknesses: 0.80 and 1.20 mm. A numerical analysis was carried out using the finite element method (FEM) through LS-DYNA code. (c) 2007 Elsevier B.V. All rights reserved.

Three Dimensional Finite Element Analyses of Oral Structures by Computerized Tomography

Our aim was to document the benefits of three dimensional finite element model generations from computed tomography data as well as the realistic creation of all oral structures in a patient. The stresses resulting from the applied load in our study did not exceed the structure limitations, suggesting a clinically acceptable physiological condition.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Determination of pore size distributions by regularization and finite element collocation

The problem of extracting pore size distributions from characterization data is solved here with particular reference to adsorption. The technique developed is based on a finite element collocation discretization of the adsorption integral, with fitting of the isotherm data by least squares using regularization. A rapid and simple technique for ensuring non-negativity of the solutions is also developed which modifies the original solution having some negativity. The technique yields stable and converged solutions, and is implemented in a package RIDFEC. The package is demonstrated to be robust, yielding results which are less sensitive to experimental error than conventional methods, with fitting errors matching the known data error. It is shown that the choice of relative or absolute error norm in the least-squares analysis is best based on the kind of error in the data. (C) 1998 Elsevier Science Ltd. All rights reserved.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. (C) 2003 Elsevier B.V. All rights reserved.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses

Objective. To evaluate the biaxial and short-beam uniaxial strength tests applied to resin composites based upon their Weibull parameters, fractographic features and stress distribution. Methods. Disk- (15 mm x 1 mm) and beam-shaped specimens (10 mm x 2 mm x 1 mm) of three commercial composites (Concept/Vigodent, CA; Heliomolar/Ivoclar-Vivadent, HE; Z250/3M ESPE, FZ) were prepared. After 48h dry storage at 37 degrees C, disks and beams were submitted to piston-on-three-balls (BI) and three-point bending (UNI) tests, respectively. Data were analyzed by Weibull statistics. Fractured surfaces were observed under stereomicroscope and scanning electron microscope. Maximum principal stress (sigma(1)) distribution was determined by finite element analysis (FEA). Maximum sigma(1-BI) and sigma(1-UNI) were compared to FZ strengths calculated by applying the average failure loads to the analytical equations (sigma(a-BI) and sigma(a-UNI)). Results. For BI, characteristic strengths were: 169.9a (FZ), 122.4b (CA) and 104.8c (HE), and for UNI were: 160.3a (FZ), 98.2b (CA) and 91.6b (HE). Weibull moduli ( m) were similar within the same test. CA and HE presented statistically higher m for BI. Surface pores ( BI) and edge flaws ( UNI) were the most frequent fracture origins. sigma(1-BI) was 14% lower than sigma(a-BI.) sigma(1-UNI) was 43% higher than sigma(a-UNI). Significance. Compared to the short-beam uniaxial test, the biaxial test detected more differences among composites and displayed less data scattering for two of the tested materials. Also, biaxial strength was closer to the material`s strength estimated by FEA. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.