1,721,042 research outputs found
A Galerkin boundary contour method for two-dimensional linear elasticity
No full textThe Boundary Contour Method (BCM) is a recent variant of the Boundary Element Method (BEM) resting on the use of boundary approximations which "a priori" satisfy the field equations. For two-dimensional problems, the evaluation of all the line-integrals involved in the collocation BCM reduces to function evaluations at
the end-points of each element, thus completely avoiding
numerical integrations.
With reference to 2-D linear elasticity, this paper develops
a variational version of BCM by transferring to the BCM context the ingredients which characterize the Galerkin-Symmetric BEM (GSBEM). The method proposed herein requires no numerical integrations: all the needed double line-integrals over boundary elements pairs can be evaluated by generating appropriate "potential functions'' (in closed form) and computing their values at the element end-points. This holds for straight as well as
curved elements; however the coefficient matrix of the
equation system in the boundary unknowns turns out to
be fully symmetric only when all the elements are straight.
The numerical results obtained for some benchmark
problems, for which analytical solutions are available,
validate the proposed formulation and the corresponding
solution procedure
Boundary element elastic analysis of layered soils by a successive stiffness method
No full textThe elastostic analysis of layered systems (such as a soil consisting of a set of L individually homogeneous strata) is tackled here on the basis of discretized boundary integral equations (boundary element method). The 'successive stiffness' method proposed is shown to imply noteworthy advantages with respect to both the standard boundary element methods by zones (or subregions) and another ad hoc, earlier method resting on a boundary element approach combined with the transfer matrix concept. This conclusion is corroborated by two-dimensional examples
Elastic-plastic boundary element analysis as a linear complementarity problem
No full textElastic-plastic constitutive laws allowing for nonassociation, corners and hardening (or softening) are formulated both in the usual terms of rates and in terms of piecewise-linear approximation (local or global).
The direct boundary element method combined with such descriptions of nonlinear material behaviour, is shown to reduce elasto-plastic structural analysis, both by infinitesimal and finite steps, to a linear complementary problem. On this basis, a general extremum characterization of the solution and conditions for solution uniqueness are pointed out.
Various solution procedures are envisaged in the new unitary framework
Dynamic shakedown and bounding theory for a class of nonlinear hardening discrete structural models
No full textShakedown analysis and bounding methods in elastic-plastic dynamics are dealt with here on the following basis: the model adopted for the constitutive (element) behavior is centered on a linear dependence of yield functions on (generalized) stresses and nonlinear dependence (hardening) of yield limits on sign-constraint internal variables which play here a central role in all developments; simple discrete structural models (basically trusses) are referred to; constrained optimization in finite dimensional spaces (nonlinear programming) is the mathematical
and computational context employed.
The contributions presented are as follows: a number of earlier results based on piecewiselinear plastic models are extended to nonlinear hardening; restrictions on the hardening rule are established for various conclusions to be valid; a systematic and unified theoretical framework is developed, so that shakedown theorems and various bounds are shown to be closely related.
The theoretical results expounded are illustrated by simple numerical examples
On boundary element - transfer matrix analysis of layered systems
No full textThe chain pattern of certain elastic systems such as layered softs lends itself to be exploited in ad hoc solution procedures. A method of this kind proposed earlier (1977, 1984) combines the boundary integral approach (in its discretised, boundary element version) and the transfer matrix concept and exhibits a special appeal as for simplicity, elegance and compactness of the final reduced equation system.
In this paper we analyse such BE-TM technique using mechanical interpretations and some notions of numerical analysis (primarily on matrix conditioning). The findings are as follows: outside of a
relatively narrow range of geometry ratios (layer thickness over a typical discretization length) certain submatrices to invert are bound to become ill-conditioned, causing significant inaccuracies in the resulting tractions; this intrinsic limitation of applicability strongly depends on the adopted computation precision. Alternative methods, which avoid such limitation but still exploit the chain pattern, are envisaged and developed in a parallel paper
Extremum theorems for finite-step backward-difference analysis of elastic-plastic nonlinearly hardening solids
No full textFor the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an effective stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of material stability are assumed
On the use of infinite elements in the analysis of two-dimensional layered elastic systems.
No full textSymmetric Galerkin BEM in 3D elasticity: computational aspects and applications to fracture mechanics
No full textElastic analysis of layered soils by boundary elements: comparative remarks on various approaches
No full textThe linear elastostatic analysis of layered soils, often required for parametric studies in preliminary design of foundations, is tackled here by various boundary integral equation approaches apt to exploit the chain pattern of the system topology
Symmetric BE method in two dimensional elasticity: evaluation of double integrals for curved elements, Computational Mechanics
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