J. Cañas

Contact problems with nonconforming discretizations using boundary element method

Abstract A procedure to solve two-dimensional frictionless contact problems between two bodies not necessarily modeled with identical discretizations is presented. The procedure is based on the boundary element method and follows a mixed incremental and iterative technique. The load is applied in a number of identical increments selected by the user for each problem. An iterative procedure to reach a compatible solution is applied for each of these increments of load, the geometry being updated after each increment. The algorithm developed is applicable to any problem belonging to the three classic contact situations: conforming, advancing and receding. Results corresponding to three cases representative of these three types of problems are finally shown.

A simplified numerical analysis of residual stresses in aluminum welded plates

The residual stresses originated in a welded Al-5083-O aluminum alloy plate are numerically studied. The thermal field is simulated by means of one analytical solution of the infinite plate, after which two thermal approaches are introduced, the temperature not changing along the welding direction in either case. The thermomechanical problem is solved by using a code based on the finite element technique (ABAQUS). The influence on the residual stresses of the strain hardening and the temperature material properties dependency has been considered. A plane stress model is used, the concordance of the numerical results thus obtained with the experimental measurements obtained using the blind hole technique being excellent. A discussion of the inability of a plain strain model to reproduce the experimental results is finally presented. The general conclusions of this study can be extended to annealed aluminum alloys (type O), whose elastic properties are not susceptible to change under heat treatment.

ON THE REMOVAL OF RIGID BODY MOTIONS IN THE SOLUTION OF ELASTOSTATIC PROBLEMS BY DIRECT BEM

A theoretical and numerical study of the removal of rigid body motions in the solution of the boundary form of Somigliana identity and of the corresponding discretized linear system of the direct BEM is presented. This study is based on the Fredholm theory of linear operators and mechanical aspects of the problem. Various methods suitable for implementation in BEM codes are analyzed and relations between apparently different methods are shown. The relation between global equilibrium conditions and solvability of the discretized linear system of the direct BEM is discussed.

Stress singularities in 2D orthotropic corners

A new technique for analysis of two-dimensional linear elastostatic solutions with stress singularities at orthotropic corners is developed. An explicit and general representation of the associated eigenequation given as ‘zero determinant condition’ of a matrix with half dimension in comparison with the current approach is derived by application of Stroh relations of anisotropic elasticity. The technique is directly applicable to anisotropic corners. Analytical formulae for stress singularity exponents, roots of the associated eigenequations, at orthotropic half-plane and semiinfinite crack problems for all combinations of basic homogeneous boundary conditions, including slip with friction, are derived. it is noteworthy that the singularity exponents are invariant with respect to the relative orientation of boundary edges and orthotropic material for nine of these combinations. Numerical analysis of singularity exponents for some configurations typical in the modelization of material tests of fiber-matrix composite materials is presented.

Interpretation of the problems found in applying contact conditions in node-to-point schemes with boundary element non-conforming discretizations

Several procedures for considering contact problems between deformable bodies using boundary elements with non-conforming discretizations are discussed in this paper. All the procedures considered (both those formerly proposed and a new one presented here) are based on an approach of strong imposition of the contact conditions, relating values of displacements and tractions of points and nodes of both bodies to force equilibrium and compatibility equations. All the procedures lead to similar results when the same general rule is followed in all cases: the body whose nodes control the displacements of the contact zone is discretized with more refined meshes. There are, nevertheless, cases, not previously referenced in the literature, where these procedures produce wrong definition of the subzones of adhesion and sliding, as well as some jumps in the stresses. These problems, whose appearance is shown to be due to the intrinsic nature of the node-to-points contact schemes, are discussed and recommendations are given to avoid them. Three classical examples belonging to the conforming, receding and advancing contact problems are studied, considering the presence and absence of friction.

Determination of G12 by means of the off-axis tension test.: Part I: review of gripping systems and correction factors

Abstract The determination of the intralaminar shear modulus G 12 in composite materials is by no means a straight forward task. Several different tests and procedures have been proposed, with the off-axis test achieving popularity as a result of its apparent simplicity. A review of the most significant studies and proposals connected with the determination of G 12 by means of the off-axis tension test is presented in this paper. The majority of the contributions can be classified in two general approaches. The first approach contains the proposals to modify the gripping system in order to allow the ideal deformation of the specimen. Particular attention is paid to the use of rotating grips and the results obtained. Reasons why other authors did not achieve satisfactory results are explored. In the second approach a coherent correction scheme, based on an iterative procedure applied to measurements obtained from the test, is presented. Finally, the dependence of the correction factor, based on the Pagano and Halpin analysis, upon the properties of the material is discussed.

A complete field method for the photoelastic determination of KI and KII in general mixed-mode fracture

A general approach based on photoelasticity to calculate the stress intensity factors KI and KII in any combination of geometry and load is developed. The procedure takes the information from both the near and the far field, using four complex functions which are developed in series expansions. The coefficients, two of them related to the stress intensity factors, are determined by a Newton-Raphson scheme coupled with a least squares procedure. Several modifications of the numerical procedure are introduced in order to reach convergence in an efficient and reliable manner. The necessity of using a total of four complex functions as well as the advisability of taking information from the whole field are emphasized by means of the study of two representative examples: a slant crack in a plate in traction and a simple supported beam with a crack along the neutral line.

A one-dimensional model for the prediction of residual stress and its relief in welded plates

The simulation of the welding process by means of continuum mechanics models has a very high cost both in input data preparation time and in computing time required for the integration of the complex thermoelastoplastic equations involved in solids with temperature dependent properties. For this reason, the plates in this study will be visualized as formed by a certain number of bars that can carry out elastoplastic behaviour and having temperature dependent properties. The thermal loads are simulated by analytical singular solutions, the thermomechanical problem being solved by means of an incremental algorithm of high efficiency. An excellent agreement has been found between the results numerically predicted and those previously obtained with an experimental technique and the Finite Element Method. Finally, the one-dimensional model developed here is used to predict the effects of a local heat treatment on the residual stresses originated by the welding. The versatility and rapidity of the use of this model makes it specially suitable to be used as a tool to select among different stress relieving procedures.

Determination of G12 by means of the off-axis tension test. Part II: a self-consistent approach to the application of correction factors

Abstract Several different tests and procedures have been proposed for the determination of the intralaminar shear modulus G 12 in composite materials. The off-axis tension test, the ±45° test and the Iosipescu test are the most widely used. The advantages of the off-axis test are the ease of specimen preparation and the simplicity of the test procedure. A detailed review of the most significant papers on the determination of G 12 by means of the off-axis test has been presented in Part I of the present study. In this paper, a new graphical procedure, based on the numerical results from a test with clamped end conditions, is introduced. The use of these graphs requires the use of clamping conditions in the tests. Thus, an experimental study, using Moire interferometry, has been carried out to check the satisfaction of this condition in the most commonly used methods of performing the test. It has been found that a specimen with bonded end tabs reproduces the most reliable clamped condition. Finally, the results of several 10° off-axis tests on a graphite–epoxy composite are presented as a demonstration of the applicability of the correction scheme proposed in a wide range of specimen aspect ratios.

Photoelastic determination ofK I andK II : A numerical study on experimental data

The most efficient photoelastic methods to obtain stress intensity factors are those based on stress functions series expansions. The coefficients of these expansions are fitted to the experimental isochromatic pattern using an overdeterministic Newton-Raphson least squares method. In this paper, a study has been carried out to analyze the influence on the results of several numerical and experimental factors. It is shown that accurate values of the stress intensity factorsKIandKIIcan be obtained by following some recommendations given in the text and summarized in the conclusions at the end of the paper.