Elastic-viscoplastic solids subjected to thermal and loading cycles; G. Linear elastic-ideal plastic as well as linear elastic-limited linear hardening material behaviour is taken into account. That theorem applies to elastic-plastic structures under time-dependent loading histories, and gives a sufficient condition for the plastic dissipation to remain bounded in time. In particular, the model of generalized standard materials gives a convenient framework to derive appropriate results for common models of plasticity with strain-hardening. If Melan's condition is satisfied, we show that shakedown indeed occurs provided the time fluctuations of the elastic moduli satisfy a certain condition which in particular is fulfilled if the time fluctuations are not too large.
In consequence, the aim of this paper is to extend existing formulations for arbitrary numbers of loading, which is inevitable for most technical applications. Consider the set of all the local values of elastic stresses associated to any feasible loading, i. The theory of shakedown suffers from two defects: geometry changes are ignored and the material behavior is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. The numerical procedure is applied to a square plate with a circular hole under variable traction in two directions, and the obtained approximations are compared with available results. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are Interior Point Methods. The theorems appear as simple as those of Melan and Koiter for perfect plasticity but applied to the much larger class of more realistic kinematic hardening materials. Over the last decades powerful numerical methods have been developed to carry out one of the oldest and most important tasks of design engineers, which is to determine the load carrying capacity of structures and structural elements.
Therefore, we had to answer ourselves three questions: Who may benefit? As a first attempt for a shakedown theory for this type of material, this theorem can give rise to variational formulations useful for numerical computations, similar to those previously used for the classical shakedown theory. The resulting nonlinear convex optimization problem is presented in a generalized formulation and then solved by an interior-point algorithm, which is characterized by a problem-tailored solution strategy, particularly suitable for application to large-scale engineering structures. We study an infinite dimensional mathematical programming problem, which arises naturally in solid mechanics. It is shown that shakedown analysis can make quite stable predictions of admissible load ranges despite the simplicity of the underlying hardening models. The Melan's theorem has the distinctive property of being path-independent, i.
Although interior-point techniques, primarily in the form of barrier methods, were widely used during the 1960s for problems with nonlinear constraints, their use for the fundamental problem of linear programming was unthinkable because of the total dominance of the simplex method. Many applications of the present algorithm for plane strain problems and tubes under variable thermomechanical loadings have already been published in3738 39, although the complete algorithm has not been described elsewhere. Since then, interior methods have advanced so far, so fast, that their influence has transformed both the theory and practice of constrained optimization. This paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function. The treatment of railway problems and the analysis and optimisation of pavements are further examples of important areas of applications. An improved boundary element analysis for the bending of a thin plate with a crack; O. Although the book is primarily concerned with a specific optimization package, the issues discussed have much wider implications for the design and implementation of large-scale optimization algorithms.
Several examples of loadings are investigated in order to test the final criterion in a variety of situations. خدمات کلان صدای رهیاب : ، ، ، برای مشاوره تحصیلی و روانشناسی میتوانید به سایت مراجعه کنید. Steady cyclic state of a structure: methods of its direct determination; D. By the early 1980s, barrier methods were almost universally regarded as a closed chapter in the history of optimization. The residual stress and residual strain of structures under shakedown conditions were obtained.
Min-max approach to shakedown and limit load analysis for elastic perfectly plastic and kinematic hardening materials; J. After explaining the theoretical foundations of their approach, the authors describe in detail the numerical scheme, in particular the underlying optimization via interior point methods. It is based on a mixed finite element approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. This way, the classical advantages of direct methods of plasticity, such as robustness, mono-parametric safety assessment and load history independence are also enabled in the field of aluminium plastic design. These methods become particularly effective with limit and shakedown analysis yielding linear limit state functions. Secondly, the corresponding discrete forms are briefly recalled. A reduced kinematic inadaptation theorem without time integrals is deduced, which is separated into incremental and alternatin plasticity collapse criteria.
An extensive series of numerical tests is presented showing the reliability of the proposed formulation. Bounds to the safety factor for elastic shakedown of structures under variable loads are considered. Next, an algorithm, based on the classical primal—dual interior point method, is developed. It is demonstrated that by maintaining a constitutively accurate description of the plastic strains the method is able to calculate strict lower bound shakedown boundaries. Min-max approach to shakedown and limit load analysis for elastic perfectly plastic and kinematic hardening materials; J. The attempt to extend the classical shakedown theory of Melan and Koiter to geometrically non-linear problems is presented in several papers.
Considering a self-equilibrated couple-stress field, it is shown that the plastic dissipation is bounded and that the material shakes down for any given combinations of loads and moments. Interior methods are a pervasive feature of the optimization landscape today, but it was not always so. Numerical examples show that the proposed method is effective and precise computationally. Mathematical modelling of plates and shells continually calls for an inexpensive compromise among crucial wishes. Numerical examples of technical relevance illustrate the proposed method.
By the early 1980s, barrier methods were almost without exception regarded as a closed chapter in the history of optimization. The various bounds and shake-down limits obtained in the paper serve as useful benchmarks for future numerical shakedown analysis, and also provide a valuable reference for the safe design of pavements. Adaptation of spherical and cylindrical vessels to variable internal pressure and temperature. Abstract: This collection of papers is a state of the art presentation of theories and methods related to the problem of the behaviour of mechanical structures under variable loads beyond their elastic limit In particular, the problems of shakedown, ratchetting, transient and asymptotic cyclic states are addressed. An indirect incremental method for a shakedown analysis based on the min-max approach; S. However, no current method exists that combines a mixed approximation of the kinematics and equilibrium with meshless methods for an elastic shakedown problem. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress.