A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Numerical methods in rock mechanics

Chaotic bat algorithm

Evolutionary computation and structural design: A survey of the state-of-the-art

Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.

Fluid Mechanics of Heart Valves

Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice–Boltzmann methods

The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).

Thus, a new procedure, based upon a bi-cubic co-ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed.

Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and-attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes.

Some illustrative examples which assess the stability and accuracy of the new formulae are included.

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A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods

Structural shape optimization 3D finite-element models based on genetic algorithms and geometric modeling

Finite elements, genetic algorithms and b-splines: a combined technique for shape optimization

The optimization of bidimensional shapes is one of the most commonly addressed problems in engineering. This work is concerned with the use of Genetic Algorithms (GAs) and β-spline-curves modeling for the optimization of Boundary Element Models (BEM). The paper briefly summarizes the basis of the GAs formulation and describes how to use refined genetic operators. The model boundary is discretized by using the BEM, and selected parts of the boundary are modeled by using β-spline curves, in order to allow easy remeshing and adaptation of the boundary to the external actions. Two numerical examples are presented and discussed in detail, showing that the proposed combined technique is able to optimize the shape of the domains with minimum computational effort. The reduction in the model area is significant, without violating the restrictions imposed to the model.

Miguel Cerrolaza

Papers

Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice–Boltzmann methods

A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods

Structural shape optimization 3D finite-element models based on genetic algorithms and geometric modeling

Finite elements, genetic algorithms and b-splines: a combined technique for shape optimization

Optimization of 2D boundary element models using β-splines and genetic algorithms