We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

In this work, we present a numerical method for solving the diffraction of transient elastic waves by cracks of arbitrary shapes in complex media, with Signorini’s boundary conditions on the crack. We use a fictitious domain method based on a mixed displacement–stress formulation for elastodynamics. We propose an off-centered time discretisation scheme for enforcing the stability.

In this paper an innovative balloon-stent design method, which conjugates 3D finite-element approach, is presented. The method is based on a large strain and large displacement formulation, with multi-objective optimization using Genetic Algorithm (GA). This procedure allows us to automatically obtain new geometries that improve stent performance and to analyze the relationship between geometri...

We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

An O(n) complexity algorithm for computing an 2-greatest common divisor (gcd) of two polynomials of degree at most n is presented. The algorithm is based on the formulation of polynomial gcd given in terms of resultant (Bézout, Sylvester) matrices, on their displacement structure and on the reduction of displacement structured matrices to Cauchy-like form originally pointed out by Georg Heinig....

This paper presents phononic band-structure calculation results obtained using a mixed variational formulation for 1-, and 2-dimensional unit cells. The formulation itself is presented in a form which is equally applicable to 3-dimensiomal cases. It has been established that the mixed-variational formulation presented in this paper shows faster convergence with considerably greater accuracy tha...

This article considers a mixed finite element method for linear elasticity. It is based on a modified mixed formulation that enforces the continuity of the stress weakly by adding a jump term of the approximated stress on interior edges. The symmetric stress are approximated by nonconforming linear elements and the displacement by piecewise constants. We establish (h) error bound in the (broken...

this paper deals with new method for designing the tuned mass dampers (tmd) with considering both transient and steady state responses, simultaneously. this formulation is presented for undamped vibrations. for this purpose, the absolute value of the structural displacement ratio is minimized numerically. this procedure leads to optimum value of tmd's specifications. for numerical verification,...

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems and independent of the const...

We introduce a novel discrete optimization method for non-rigid image registration based on the random walker algorithm. We discretize the space of deformations and formulate registration using a Gaussian MRF where continuous labels correspond to the probability of a point having a certain discrete deformation. The interaction (regularization) term of the corresponding MRF energy is convex and ...