Shape derivatives of energy and regularity of minimizers for shallow elastic shells with cohesive cracks

2022 ◽  
Vol 65 ◽  
pp. 103505
Author(s):  
Viktor Shcherbakov
Keyword(s):  
Elastic Shells ◽  
Shape Derivatives ◽  
Regularity Of Minimizers ◽  
Derivatives Of

On Saint Venant’s Principle: Elastic Shells and Plates

1960 ◽  
Vol 27 (3) ◽  
pp. 417-422 ◽  
Author(s):  
P. M. Naghdi
Keyword(s):  
Fixed Point ◽  
Integral Formula ◽  
Middle Surface ◽  
The Other ◽  
Elastic Shells ◽  
Partial Derivatives ◽  
Other Hand ◽  
Derivatives Of ◽  
Surface Loads

This investigation is concerned with an examination of the validity of Saint Venant’s principle in the theory of thin elastic shells and plates. With the aid of an integral formula derived for the displacements and their relevant partial derivatives of all orders at a fixed point of the shell middle surface, the conclusions reached may be roughly stated as follows: If the loads acting on the shell maintained in equilibrium are purely edge loads, then the orders of magnitude of the displacements and stresses are in accord with the traditional statement of Saint Venant’s principle. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of the modified Saint Venant principle.

scholarly journals Shape derivatives for an augmented Lagrangian formulation of elastic contact problems

2020 ◽  
Author(s):  
Bastien Chaudet-Dumas ◽  
Jean Deteix
Keyword(s):  
Augmented Lagrangian ◽  
Sufficient Conditions ◽  
Contact Problems ◽  
Lagrangian Formulation ◽  
Directional Derivatives ◽  
Practical Reasons ◽  
Process Conditions ◽  
Shape Derivatives ◽  
Derivatives Of ◽  
Augmented Lagrangian Formulation

This work deals with shape optimization of an elastic body in sliding contact (Signorini) with a rigid foundation. The mechanical problem is written under its augmented Lagrangian formulation, then solved using a classical iterative approach. For practical reasons we are interested in applying the optimization process with respect to an intermediate solution produced by the iterative method. Due to the projection operator involved at each iteration, the iterate solution is not classically shape differentiable. However, using an approach based on directional derivatives, we are able to prove that it is conically differentiable with respect to the shape, and express sufficient conditions for shape differentiability. Finally, from the analysis of the sequence of conical shape derivatives of the iterative process, conditions are established for the convergence to the conical derivative of the original contact problem.

Analytical Shape Derivatives of the MFIE System Matrix Discretized With RWG Functions

2013 ◽  
Vol 61 (2) ◽  
pp. 985-988 ◽  
Author(s):  
Juhani Kataja ◽  
Athanasios G. Polimeridis ◽  
Juan R. Mosig ◽  
Pasi Yla-Oijala
Keyword(s):  
System Matrix ◽  
Shape Derivatives ◽  
Derivatives Of
Sign in / Sign up

Export Citation Format

Share Document