Safe Load Condition Research Articles

Quasistatic viscoplasticity without safe-load conditions

In the paper we present the existence theory to gradient-type quasistatic models of viscoplasticity. Our goal is to show the reader a new point of view to the existence of solutions to such models where no safe-load conditions are needed. In the classic approach authors use this kind of indirect assumption on data in order to obtain proper energy estimates, in our approach we propose how to omit such safe-load conditions by quite delicate estimates and due to considering a proper approximation of the initial problem.

Optimal control of perfect plasticity part I: Stress tracking

<p style='text-indent:20px;'>The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system admits a solution, whose stress field is unique. This gives rise to a well defined control-to-state operator, which is continuous but not Gâteaux differentiable. The control-to-state map is therefore regularized, first by means of the Yosida regularization resp. viscous approximation and then by a second smoothing in order to obtain a smooth problem. The approximation of global minimizers of the original non-smooth optimal control problem is shown and optimality conditions for the regularized problem are established. A numerical example illustrates the feasibility of the smoothing approach.</p>

On strong solutions of viscoplasticity without safe-load conditions

In this paper we discuss existence of pointwise solutions for dynamical models of viscoplasticity. Among other things, this work answers the question about necessity of safe-load conditions in case of viscoplasticity, which arise in the paper of K. Chełmiński (2001) [11]. We proved that solutions can be obtained without assuming any kind of safe-load conditions. Moreover, in the manuscript we consider much more general model than in the above mentioned paper. Namely, we consider the model with mixed boundary conditions and we allow a possible disturbance of the inelastic constitutive function by a globally Lipschitz function. Presented approach shows that via the same methods one can prove existence of pointwise solutions for: coercive models, self-controlling models, models with polynomial growth (not necessary of single valued) and monotone-gradient type models of viscoplasticity.

Prandtl–Reuss dynamical elasto-perfect plasticity without safe-load conditions

In this article we study the existence theory to the Prandtl–Reuss dynamical model of elasto-perfect plasticity with non-homogeneous mixed boundary conditions. By using only the Yosida approximation of inelastic constitutive multifunction we are able to prove the existence of solutions without assuming any kind of safe-load conditions, which are quite common in the theory of elasto-perfect plasticity.

Fatigue life prediction of heavy vehicle suspension system under varying load conditions

Leaf spring experiences frequent cyclic loading during working conditions. When design stage itself it is very essential to assess the fatigue life of the suspension system. It is important to consider and evaluate the key aspects of fatigue failure and life by using Finite Element Analysis (FEA) techniques to overcome these failures. This paper serves to stimulate the premature failure of the existing and proposed bracket model with generalized force elements under dynamic load conditions. Scanning Electron Microscope (SEM) was used to identify the bracket failure prone areas which indicate that the cyclic load in the suspension system is caused by rural area road-induced vibrations and bumps. This contributes to the increase of the fatigue fracture, which ends up with a bracket failure. The results indicated that the fatigue life of existing bracket is low for rough road conditions; the modified bracket has been optimized for the safe load conditions of the heavy vehicle suspension system

Collapse mechanisms and the existence of equilibrium solutions for masonry bodies

The equilibrium equations of no-tension (masonry-like) bodies are analyzed. Unlike the existing proofs of the existence of the solution by Anzellotti or Giaquinta and Giusti, the present proof does not employ the uniform safe load condition. It is based on the assumption of the absence of a suitably defined collapse mechanisms. The collapse mechanism belongs to a generalized space BD(cl Ω) of displacements of bounded deformation on the closure cl Ω of the body Ω. This generalized displacement can have a jump discontinuity on the boundary of the body and the generalized strain is a measure on the closure of the body (instead of the standard interpretation as a measure supported by the interior). The equilibrium solution, however, belongs to the classical space of displacements of bounded deformation BD(Ω).

A VARIATIONAL PRINCIPLE FOR PLASTIC HINGES IN A BEAM

We focus on a variational model of an elastic–plastic beam which is clamped at both endpoints and subject to a transverse L∞ load: the mathematical formulation is a 1D free discontinuity problem with second-order energy dependent on gradient-jump integrals but not on the cardinality of gradient-discontinuity set. The related energy is not lower semicontinuous in BH; moreover the relaxed energy is finite also when second derivatives have Cantor part. Nevertheless we show that if a safe load condition is fulfilled, then minimizers exist and they actually belong to SBH, say their second derivative has no Cantor part. If in addition a stronger condition on load is fulfilled, then minimizer is unique and belongs to H2. Moreover, we can always select one minimizer whose number of plastic hinges does not exceed 2 and is the limit of minimizers of penalized problems. When the load stays in the gap between safe load and regularity condition, then minimizers with hinges are allowed; if in addition the load is symmetric and strictly positive, then there is uniqueness of minimizer, the hinges of such minimizer are exactly two and they are located at the endpoints.

Numerical Enclosures for Variational Inequalities

AbstractWe present a new method for proving the existence of a unique solution of variational inequalities within guaranteed close error bounds to a numerical approximation. The method is derived for a specific model problem featuring most of the difficulties of perfect plasticity. We introduce a finite element method for the computation of admissible primal and dual solutions which a posteriori guarantees the existence of a unique solution (by the verification of the safe load condition) and which allows determination of a guaranteed error bound. Finally, we present explicit existence results and error bounds in some significant specific configurations.

Global existence of weak‐type solutions for models of monotone type in the theory of inelastic deformations

AbstractThis article introduces the notion of weak‐type solutions for systems of equations from the theory of inelastic deformations, assuming that the considered model is of monotone type (for the definition see [Lecture Notes in Mathematics, 1998, vol. 1682]). For the boundary data associated with the initial‐boundary value problem and satisfying the safe‐load condition the existence of global in time weak‐type solutions is proved assuming that the monotone model is rate‐independent or of gradient type. Moreover, for models possessing an additional regularity property (see Section 5) the existence of global solutions in the sense of measures, defined by Temam in Archives for Rational Mechanics and Analysis, 95: 137, is obtained, too. Copyright © 2002 John Wiley & Sons, Ltd.

Strong solution for an elastic-plastic plate

Given a regular bounded open setΩ ⊂R 2,λ, μ>0 andg eL q (Ω) withq>2, we prove, under compatibility and safe load conditions ong, the existence of a minimizing pair for the functional , over closed setsK ⊂ ℝ2 and functionsu e C0( $$\overline \Omega $$ ) ∩ C2(Ω/K); here ¦[Du]¦ denotes the jump ofDu acrossK and ℋ1 is the 1-dimensional Hausdorff measure.

The obstacle problem for an elastoplastic body

The obstacle problem for elastoplastic bodies is considered within the framework of general existence results for unilateral problems recently presented by Baiocchiet al. Two models of plasticity are considered: one is based on a displacement-plastic strain formulation and the second, a specialization of the first, is the standard Hencky model. Existence theorems are given for the Neumann problem for a body constrained to lie on or above the half-space {x∈ℝ3:x3≤0}. For hardening materials the displacements are sought in the Sobolev spaceH1(Ω, ℝ3) while for perfectly plastic materials they are sought in BD(Ω), the space of functions of bounded deformation. Conditions for the existence of solutions are given in terms of compatibility and safe load conditions on applied loads.

Dual spaces of stresses and strains, with applications to Hencky plasticity

We prove the existence of a dual pairing between admissible stress and displacement fields in the context of Hencky plasticity. We apply this to show (i) that an extremal displacement field exists whenever the safe load condition holds; and (ii) that any extremal stress and displacement fields are related by a "saddle point condition," expressing in weak form the constitutive hypothesis of Hencky plasticity.