scholarly journals CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA
Keyword(s):  
Lagrange Multipliers ◽  
Variational Equation ◽  
Small Deformation ◽  
Contact Problems ◽  
Point Theory ◽  
The Body ◽  
Elastic Materials ◽  
Weak Formulation ◽  
Nonlinearly Elastic ◽  
Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

Optimal control for antiplane frictional contact problems involving nonlinearly elastic materials of Hencky type

2017 ◽  
Vol 23 (3) ◽  
pp. 308-328 ◽  
Author(s):  
Andaluzia Matei ◽  
Sorin Micu ◽  
Constantin Niţǎ
Keyword(s):  
Optimal Control ◽  
Frictional Contact ◽  
Variational Equation ◽  
Optimal Solution ◽  
Contact Problems ◽  
Point Of View ◽  
Friction Laws ◽  
Convergence Results ◽  
Positive Exponent ◽  
Nonlinearly Elastic

We consider an antiplane contact problem modeling the friction between a nonlinearly elastic body of Hencky type and a rigid foundation. We discuss the well-posedness of the model by considering two friction laws. Firstly, Tresca’s law is used to describe the friction force and leads to a variational inequality. Alternatively, a regularizing power law with a positive exponent r is considered and gives, from the mathematical point of view, a variational equation. In both contexts, we address a boundary optimal control problem by minimizing, on a nonconvex set, a cost functional with two arguments. We show the existence of at least one optimal pair for each problem. Finally, we deliver some convergence results proving that the optimal solution of the regular problem tends, when r goes to zero, to an optimal solution of the first one.

On the solvability of mixed variational problems with solution-dependent sets of Lagrange multipliers

2013 ◽  
Vol 143 (5) ◽  
pp. 1047-1059 ◽  
Author(s):  
Andaluzia Matei
Keyword(s):  
Lagrange Multipliers ◽  
Frictional Contact ◽  
Variational Equation ◽  
Deformable Body ◽  
Variational Problems ◽  
Abstract Result ◽  
Continuous Maps ◽  
Mixed Variational Problem ◽  
Fixed Point Technique ◽  
Weak Solvability

We study an abstract mixed variational problem, the set of the Lagrange multipliers being dependent on the solution. The problem consists of a system of a variational equation and a variational inequality. We prove the existence of the solution based on a fixed-point technique for weakly sequentially continuous maps. We then apply the abstract result to the weak solvability of a boundary-value problem that models the frictional contact between a cylindrical deformable body and a rigid foundation.

A Rapture of the Nerds? A Comparison between Transhumanist Eschatology and Christian Parousia

2019 ◽  
Vol 24 (2) ◽  
pp. 343-367
Author(s):  
Roberto Paura
Keyword(s):  
Human Brain ◽  
Point Theory ◽  
The Body ◽  
Christian Theology ◽  
Human Beings ◽  
Human Species ◽  
The Future ◽  
The Creation ◽  
The Universe

Transhumanism is one of the main “ideologies of the future” that has emerged in recent decades. Its program for the enhancement of the human species during this century pursues the ultimate goal of immortality, through the creation of human brain emulations. Therefore, transhumanism offers its fol- lowers an explicit eschatology, a vision of the ultimate future of our civilization that in some cases coincides with the ultimate future of the universe, as in Frank Tipler’s Omega Point theory. The essay aims to analyze the points of comparison and opposition between transhumanist and Christian eschatologies, in particular considering the “incarnationist” view of Parousia. After an introduction concern- ing the problems posed by new scientific and cosmological theories to traditional Christian eschatology, causing the debate between “incarnationists” and “escha- tologists,” the article analyzes the transhumanist idea of mind-uploading through the possibility of making emulations of the human brain and perfect simulations of the reality we live in. In the last section the problems raised by these theories are analyzed from the point of Christian theology, in particular the proposal of a transhuman species through the emulation of the body and mind of human beings. The possibility of a transhumanist eschatology in line with the incarnationist view of Parousia is refused.

Estimation of the Crack Propagation Direction of a Crack Touching the Interface between Two Elastic Materials

2007 ◽  
Vol 567-568 ◽  
pp. 225-228 ◽  
Author(s):  
Luboš Náhlík ◽  
Lucie Šestáková ◽  
Pavel Hutař
Keyword(s):  
Crack Propagation ◽  
Protective Coatings ◽  
The Body ◽  
Elastic Behavior ◽  
Layered Composites ◽  
The Finite Element Method ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Composites Materials ◽  
Elastic Fracture

The objective of the paper is to investigate the direction of a further crack propagation from the interface between two elastic materials. The angle of crack propagation changes when the crack passes the interface. The suggested procedure makes it possible to estimate an angle of propagation under which the crack will propagate into the second material. The assumptions of linear elastic fracture mechanics and elastic behavior of the body with interfaces are considered. The finite element method was used for numerical calculations. The results obtained might contribute to a better understanding of the failure of materials with interfaces (e.g. layered composites, materials with protective coatings) and to a more reliable estimation of the service life of such structures.

Parallel Algorithm for Modeling Constrained Multi-Flexible Body System Dynamics

2013 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Jeremy Laflin
Keyword(s):  
Parallel Implementation ◽  
Equations Of Motion ◽  
Small Deformation ◽  
The Body ◽  
Deformation Field ◽  
Flexible Body ◽  
Disassembly Process ◽  
Joint Constraints ◽  
Kinematic Loop ◽  
Kinematic Joint

This paper presents an algorithm for modeling the dynamics of multi-flexible body systems in closed kinematic loop configurations where the component bodies are modeled using the large displacement small deformation formulation. The algorithm uses a hierarchic assembly disassembly process in parallel implementation and a recursive assembly disassembly process in serial implementation to achieve highly efficient simulation turn-around times. The operational inertias arising from the rigid body modes of motion at the joint locations on a component body are modified to account for the nonlinear inertial effects and body forces arising from the body based deformations. Traditional issues, such as motion induced stiffness and temporal invariance of deformation field related inertia terms, are robustly addressed in this algorithm. The algorithm uses a mixed set of coordinates viz. (i) absolute coordinates for expressing the equations of motion of a body fixed reference frame, (ii) relative or internal coordinates to express the kinematic joint constraints and (iii) body fixed coordinates to account for the body’s deformation field. The kinematic joint constraints and the closed loop constraints are treated alike through the formalism of relative coordinates, joint motion spaces and their orthogonal complements. Verification of the algorithm is demonstrated using the planar fourbar mechanism problem that has been traditionally used in literature.

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