A Unified Characterization of Nonunique Response in Elastic/Perfectly-Plastic and Elastic/Locking Structures Using Constraint Qualifications1
نویسندگان
چکیده
Mathematical programming methods have traditionally been used extensively in the analysis and design of elastic/plastic structures. However, some of the recent results from parametric nonlinear programming have not been fully exploited in mechanical applications, particularly those relating to the causes of singularities due to parametric variations. In this paper, we reexamine the phenomenon of nonunique displacements in elastic/perfectly-plastic structures under proportional loading. Once the analysis model as derived from a minimum energy principle is formulated as a quadratic program, it turns out that the response can be characterized as being unique or nonunique depending on the satisfaction of the linear independence or the Mangasarian-Fromovitz constraint qualification. A completely analogous result is then also derived for elastic/locking structures, thus indicating the usefulness of constraint qualifications in analyzing the nonunique behavior in other applications as well. 1submitted to the Intl. Journal of Solids and Structures 2corresponding author 1
منابع مشابه
Numerical Analysis of the Effect of External Circumferential Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM – Elastic-Plastic Behavior
The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal press...
متن کاملCauses and Consequences of Nonuniqueness in an Elastic/Perfectly-Plastic Truss
A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first-order nonlinear terms in the equilibrium equations is...
متن کاملA Closed-form Semi-analytical Elastic-Plastic Solution for Predicting the Onset of Flange Wrinkling in Deep-drawing of a Two-layered Circular Plate
In this paper to predict the critical conditions for onset of elastic-plastic wrinkling of flange of a two-layered circular blank during the deep-drawing process a closed-form semi-analytical elastic-plastic solution using Tresca yield criterion alongwith deformation theory in plasticity with considernig the perfectly plastic behaviour of materials is presented. Simplifying the presented soluti...
متن کاملElastic-Plastic Transition of Pressurized Functionally Graded Orthotropic Cylinder using Seth’s Transition Theory
In this paper the radial deformation and the corresponding stresses in a functionally graded orthotropic hollow cylinder with the variation in thickness and density according to power law and rotating about its axis under pressure is investigated by using Seth's transition theory. The material of the cylinder is assumed to be non-homogeneous and orthotropic. This theory helps to achieve better ...
متن کاملElastic-Plastic Analysis of Bending Moment – Axial Force Interaction in Metallic Beam of T-Section
This study derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering elastic-plastic idealizations. The interaction relations can predict strains, which is not possible in a rigid perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-se...
متن کامل