Qing-Hua Qin

Methods of Fundamental Solutions in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods, the mechanics of solids and structures, the basics of fundamental solutions and radical basis functions, meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications.

Research on bone remodeling has resulted in much new information and has led to improvements in design and biomedical practices. Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects presents a unified exploration of recent advances, giving readers a sound understanding of bone remodeling and its mathematical representation. Beginning with a description of the basic concept of bone remodeling from a mathematical point of view, the book details the development of each of the techniques and ideas. From there it progresses to the derivation and construction of multifield and cellular bone remodeling and shows how they arise naturally in response to external multifield loads. Topics include: Fundamental concepts and basic formulations for bone remodeling Applications of formulations to multifield internal bone remodeling of inhomogeneous long cylindrical boneTheory and solution of multifield surface bone remodelingA hypothetical regulation mechanism on growth factors for bone modeling and remodeling under multifield loadingThe RANK–RANKL–OPG pathway and formulation for analyzing the bone remodeling process A model of bone cell population dynamics for cortical bone remodeling under mechanical and pulsed electromagnetic stimulusRecent developments in experiments with bone materialsReaders will benefit from the thorough coverage of general principles for each topic, followed by detailed mathematical derivations and worked examples, as well as tables and figures where appropriate. The book not only serves as a reliable reference but is also destined to attract interested readers and researchers to a field that offers fascinating and technologically important challenges.

Research on bone remodeling has resulted in much new information and has led to improvements in design and biomedical practices. Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects presents a unified exploration of recent advances, giving readers a sound understanding of bone remodeling and its mathematical representation. Beginning with a description of the basic concept of bone remodeling from a mathematical point of view, the book details the development of each of the techniques and ideas. From there it progresses to the derivation and construction of multifield and cellular bone remodeling and shows how they arise naturally in response to external multifield loads. Topics include: Fundamental concepts and basic formulations for bone remodeling Applications of formulations to multifield internal bone remodeling of inhomogeneous long cylindrical boneTheory and solution of multifield surface bone remodelingA hypothetical regulation mechanism on growth factors for bone modeling and remodeling under multifield loadingThe RANK–RANKL–OPG pathway and formulation for analyzing the bone remodeling process A model of bone cell population dynamics for cortical bone remodeling under mechanical and pulsed electromagnetic stimulusRecent developments in experiments with bone materialsReaders will benefit from the thorough coverage of general principles for each topic, followed by detailed mathematical derivations and worked examples, as well as tables and figures where appropriate. The book not only serves as a reliable reference but is also destined to attract interested readers and researchers to a field that offers fascinating and technologically important challenges.

Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson’s equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems.The book begins with an introduction to the hybrid-Trefftz (HT) FEM that covers basic concepts and general element formulations of the method. It then concentrates on both the essentials and subroutines of MATLAB and C programming. The next few chapters present applications of T-elements to potential problems and linear plane elasticity, discuss how to solve body force in elasticity through radial basis functions, and examine how special purpose functions can be constructed. The final chapter explores advanced topics, such as the construction of Trefftz p-elements, dimensionless transformation, and an alternative formulation to HT FEM. Unifying the computer programming aspects of the Trefftz FEM, this book will stimulate the development and application of this novel method in many facets of practical engineering.