In the perspective of homogenization theory, strain-gradient elasticity is a strategy to describe overall behavior materials with coarse mesostructure. this approach, effect mesostructure described by use three tensors whose orders vary from 4 6. Higher-order constitutive make it possible rich physical phenomena. However, these objects have intricate algebraic structures that prevent us having ...

In this paper, we study the deep Ritz method for solving linear elasticity equation from a numerical analysis perspective. A modified formulation using $H^{1/2}(\Gamma_D)$ norm is introduced and analyzed in order to deal with (essential) Dirichlet boundary condition. We show that resulting provides best approximation among set of neural network (DNN) functions respect ``energy'' norm. Furthermo...

The conventional Cobb-Douglas production function model require strong assumptions such as the constant elasticity and the entire frontier efficiency. The varying elasticity production function is an useful extension but it does not take frontier efficiency into account, and the data envelope analysis model involves the use of linear programming methods to estimate the frontier efficiency where...

The present paper introduces a mixed stress-displacement method for linear elasticity, as an extension of the work performed by Christiansen [15] for computational relativity. Moreover, we establish self-adjointness in a special sense and perform numerical simulations to assess the relevance of the method, including comparison with the recent TDNNS [30, 34] mixed formulation. Extensions to high...

This paper is concerned with the convergence of mortar methods applied to linear elasticity. We prove that the conventional meshdependent norms used in the analysis of mortar methods are bounded below by the BV norm. When combined with standard results, this bound establishes a decomposition-independent and mesh-independent proof of the convergence of mortar methods in linear elasticity. 2005 E...

Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse...