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Regularization Procedure (regularization + procedure)

Distribution by Scientific Domains
Engineering40%

Selected Abstracts

Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002
Jacob Fish
Abstract Non-local dispersive model for wave propagation in heterogeneous media is derived from the higher-order mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space,time co-ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long-term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth-order differential equation, also known as a ,bad' Boussinesq problem. Regularization procedures are then introduced to construct the so-called ,good' Boussinesq problem, where the need for C1 continuity is eliminated. Numerical examples are presented to validate the present formulation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Regularized sequentially linear saw-tooth softening model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7-8 2004
Jan G. Rots
Abstract After a brief discussion on crack models, it is demonstrated that cracking is often accompanied by snaps and jumps in the load,displacement response which complicate the analysis. This paper provides a solution by simplifying non-linear crack models into sequentially linear saw-tooth models, either saw-tooth tension-softening for unreinforced material or saw-tooth tension-stiffening for reinforced material. A linear analysis is performed, the most critical element is traced, the stiffness and strength of that element are reduced according to the saw-tooth curve, and the process is repeated. This approach circumvents the use of incremental,iterative procedures and negative stiffness moduli and is inherently stable. The main part of the paper is devoted to a regularization procedure that provides mesh-size objectivity of the saw-tooth model. The procedure is similar to the one commonly used in the smeared crack framework but, in addition, both the initial tensile strength and the ultimate strain are rescaled. In this way, the dissipated fracture energy is invariant with respect not only to the mesh size, but also to the number of saw-teeth adopted to discretize the softening branch. Finally, the potential of the model for large-scale fracture analysis is demonstrated. A masonry façade subjected to tunnelling induced settlements is analysed. The very sharp snap-backs associated with brittle fracture of the façade automatically emerge with sequentially linear analysis, whereas non-linear analysis of the façade using smeared or discrete crack models shows substantial difficulties despite the use of arc-length schemes. Copyright © 2004 John Wiley & Sons, Ltd. [source]

The auto-correlation equation on the finite interval

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2003
L. Von Wolfersdorf
Applying the Fourier cosine transformation, the quadratic auto-correlation equation on the finite interval [0,T] of the positive real half-axis ,+ is reduced to a problem for the modulus of the finite complex Fourier transform of the solution. From the solutions of this problem L2 -solutions of the auto-correlation equation are obtained in closed form. Moreover, as in the case of the equation on ,+ a Lavrent'ev regularization procedure for the auto-correlation equation is suggested. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A regularization procedure for the auto-correlation equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2001
L. Von Wolfersdorf
The paper deals with the auto-correlation equation and its regularization by means of a Lavrent'ev regularization procedure in L2. The solution of this quadratic integral equation of the first kind and of the regularized equation of the second kind are obtained by reduction to a boundary value problem for the Fourier transform of the solution. We prove convergence of the approximate solution to the exact solution and derive a stability estimate for the error. Copyright © John Wiley & Sons, Ltd. [source]