Clifford algebra valued boundary integral equations for three-dimensional elasticity

Liu, Li Wei; Hong, Hong Ki

doi:10.1016/j.apm.2017.09.031

Cited by 21 publications

(12 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is worth noting that the close connection among the formulas obtained in the above theorems and formula (10) established in Liu and Hong, where the authors have made use of a different rewriting of by appealing to a Dirac operator D constructed over the orthogonal pseudo‐euclidean space

R^{3, 0}

. The main difference between them lies in the fact that the third term in Liu and Hong is monogenic (w.r.t. D ) while our third term is just harmonic and inframonogenic at once, ie, belongs to

scriptH false(normalΩ false) \cap scriptI false(normalΩ false)

.…”

Section: Resultsmentioning

confidence: 90%

“…The application of quaternionic ψ ‐hyperholomorphic functions in

R^{3}

, where ψ denotes a structural set (see Shapiro and Vasilevski, is natural in establishing a new representation for the general solution of the Lamé‐Navier system , a fact that has already been noticed in the literature, for instance. There are also several works about the application of Clifford analysis to the elastic material, including the classical book as well as the more recent papers …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inframonogenic functions and their applications in 3‐dimensional elasticity theory

García

Blaya

et al. 2018

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we consider functions satisfying the sandwich equation ∂x_f∂x_=0, where ∂x_ stands for the Dirac operator in Rm. Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of ∂x_. In particular, for odd m, we prove that a C2‐function is both inframonogenic and harmonic in normalΩ⊂Rm if and only if it can be represented in Ω as f=f1+f2+f3xtrue_+xtrue_f4, where f1 and f2 are, respectively, left and right monogenic functions in Ω, while f3 and f4 are two‐sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé‐Navier system in R3.

show abstract

R^{3, 0}

. The main difference between them lies in the fact that the third term in Liu and Hong is monogenic (w.r.t. D ) while our third term is just harmonic and inframonogenic at once, ie, belongs to

scriptH false(normalΩ false) \cap scriptI false(normalΩ false)

.…”

Section: Resultsmentioning

confidence: 90%

“…The application of quaternionic ψ ‐hyperholomorphic functions in

R^{3}

Section: Introductionmentioning

confidence: 99%

Inframonogenic functions and their applications in 3‐dimensional elasticity theory

García

Blaya

et al. 2018

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The application of ψ ‐hyperholomorphic functions in

R^{3}

, where ψ denotes a structural set (see Shapiro and Vasilevski), is natural in establishing a new representation for the general solution of the Lamé‐Navier system , a fact that has already been noticed in previous studies, for instance. There are also several works about the application of Clifford analysis to the elastic material, including the classical book and the more recent papers …”

Section: Universal Solutions Of the Lamé Systemmentioning

confidence: 97%

Decomposition of inframonogenic functions with applications in elasticity theory

García

Blaya

et al. 2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we consider functions satisfying the sandwich equation x x = 0, where x stands for the Dirac operator in R m . Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, nullIn particular, for odd m, we prove that a C 2 -function is both inframonogenic and harmonic in Ω ⊂ R m if and only if it can be represented in Ω aswhere f 1 and f 2 are, respectively, left and right monogenic functions in Ω, while f 3 and f 4 are two-sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé-Navier system in R 3 .

show abstract

“…Расчетная модель -трехмерная (пространственная) задача теории упругости. Математическая постановка этой задачи приведена, например, в [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Пусть : -область, занимаемая рассматрива-емой конструкцией, …”

Section: расчетная модель и общая постановка задачиunclassified

About Solution of Multipoint Boundary Problems of Three-Dimensional Structural Analysis With the Use of Combined Application of Finite Element Method and Discrete-Continual Finite Element Method. Part 1: Formulation and Basic Principles of Approximation

Akimov

Negrozov

2018

IJCCSE

View full text Add to dashboard Cite

1 Российская академия архитектуры и строительных наук, г. Москва, РОССИЯ 2 ЗАО «Научно-исследовательский центр «СтаДиО», г. Москва, РОССИЯ 3 Томский государственный архитектурно-строительный университет, г. Томск, РОССИЯ 4 Российский университет дружбы народов, г. Москва, РОССИЯ 5 Национальный исследовательский Московский государственный строительный университет, г. Москва, РОССИЯ Аннотация: В настоящей статье рассматриваются постановка и общие принципы аппроксимации много-точечной краевой задачи статического расчета трехмерной конструкции на основе совместного примене-ния метода конечных элементов и дискретно-континуального метода конечных элементов. В частности, описаны основные обозначения и соглашения, представлены расчетная модель и общая постановка зада-чи (на основе трехмерной теории упругости), общие принципы аппроксимации области, принятые пра-вила нумерации подобластей, правила нумерации конечных элементов и дискретно-континуальных ко-нечных элементов; описано построение дискретной (конечноэлементной) и дискретно-континуальной аппроксимирующих моделей на подобластях.Ключевые слова: дискретно-континуальный метод конечных элементов, метод конечных элементов, расчеты строительных конструкций, трехмерные задачи, постановки задач, аппроксимация ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF THREE-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 1: FORMULATION AND BASIC PRINCIPLES OF APPROXIMATION Abstract:The distinctive paper is devoted to formulation and basic principles of approximation of multipoint boundary problem of static analysis of three-dimensional structure with the use of combined application of finite element method and discrete-continual finite element method. Basic notation system, design model, general for-

show abstract

Clifford algebra valued boundary integral equations for three-dimensional elasticity

Cited by 21 publications

References 32 publications

Inframonogenic functions and their applications in 3‐dimensional elasticity theory

Inframonogenic functions and their applications in 3‐dimensional elasticity theory

Decomposition of inframonogenic functions with applications in elasticity theory

About Solution of Multipoint Boundary Problems of Three-Dimensional Structural Analysis With the Use of Combined Application of Finite Element Method and Discrete-Continual Finite Element Method. Part 1: Formulation and Basic Principles of Approximation

Contact Info

Product

Resources

About