检索结果-内蒙古大学图书馆

Two-phase Steady-state Green's Function for Orthotropic Poro-thermoelastic Materials with potential theory method

TRANSPORT IN POROUS MEDIA 2022年第3期145卷 719-744页

作者： Tariq, Muzammal Hameed Dang, Huayang Ren, Jingli Zhengzhou Univ Henan Acad Big Data Sch Math & Stat Zhengzhou 450001 Peoples R China Zhengzhou Univ Sch Mech & Engn Sci Zhengzhou 450001 Peoples R China

Green's functions for two-phase materials play a vital role in both applied and theoretical studies of solid physics. These functions are fundamental constituents in a lot of areas. In this article, we explore two-dimensional (2D) general solution for two-phase orthotropic poro-thermoelastic (PTE) materials. The operator theory, the superposition principle, and Almansi's theorem are used to develop complete general solutions of the corresponding governing equations, which satisfy the eighth-order homogeneous partial differential equations (PDEs) concerning harmonic functions. The Green's function for a steady line fluid and heat sources within two-phase orthotropic PTE material is examined by employing these compact general solutions. As a result, eight new harmonic functions with unknown constants are produced. These constants are determined under continuous and equilibrium conditions. The values of the corresponding coupled field is derived by inserting harmonic functions into the general solution. Consequently, the exact and complete solutions of the coupled field are expressed in terms of elementary functions which serve as standards for various forms of approximate and numerical solutions. Also, numerical simulations are performed using general solutions, and graphs are drawn through contours to illustrate physical mechanisms. In addition, the effect of anisotropy on pore pressure and temperature are also presented.

关键词： General solution Green's functions Orthotropic Poro-thermoelasticity Two-phase materials potential theory method

来源：评论

学校读者我要写书评

暂无评论

Exploring Two-Point Liquid Loading Effects on Transversely Isotropic Poroelastic Media Through Green's Functions Analysis

引用

TRANSPORT IN POROUS MEDIA 2025年第5期152卷 1-15页

作者： Tariq, Muzammal Hameed Zhou, Yue-Ting Tongji Univ Sch Aerosp Engn & Appl Mech Shanghai 200092 Peoples R China Shanghai Inst Aircraft Mech & Control 100 Zhangwu Rd Shanghai 200092 Peoples R China

Green's functions for two-point liquid sources analyze anisotropic mechanical-fluid interactions, providing insights for real-world applications and enabling precision in design optimization across geomechanics and biomechanics. In this paper, we uniquely derive the expression for a two-point fluid source influenced by poroelasticity in an infinite transversely isotropic material, providing a novel contribution to the literature. Initially, we obtain the general solution for the governing equations using the potential theory method with Almansi's theorem. Subsequently, building on the general solution, we derive a fundamental solution for a two-point fluid source using harmonic functions with undetermined constants. These constants are determined through continuous and equilibrium conditions. The resulting exact solutions serve as benchmarks for numerical codes and approximate solutions, offering crucial support for a wide range of project problems. To provide further insight, we present complex numerical examples illustrating the physical mechanisms through contours. Results show symmetry around two-point fluid sources, with higher magnitudes and sign changes indicating compression and expansion zones. Zero contours and inflection points are identified, while coupling effects diminish in the far field and become singular at the sources, providing valuable insights into their spatial extent and intensity. To validate our results, we compare them with existing literature, enhancing the credibility of our approach and contributing to the ongoing dialog in the field.

关键词： Two-point fluid source General solution Poroelasticity Transversely isotropic material potential theory method

来源：评论

学校读者我要写书评

暂无评论

Investigating the 3D coupling of mechanical and electrical effects on porous materials via Green's function

引用

MECHANICS RESEARCH COMMUNICATIONS 2025年 144卷

Porous materials, characterized by fluid-filled interconnected voids, exhibit intricate mechanical-electrical interactions that are essential for understanding and advancing their conductivity, strength, and engineering applications. This study introduces a comprehensive novel analysis of three-dimensional (3D) transversely isotropic poro-piezoelastic (PPE) materials, employing potential theory, displacement functions, operator theory, and Almansi's theorem. Compact general solutions are derived using harmonic functions that satisfy weighted harmonic and octaharmonic partial differential equations (PDEs). A 3D Green's function for concentrated forces and point charges in solid and fluid phases is developed, introducing four new harmonic functions to address diverse practical challenges. Numerical results, validated against existing literature, reveal distinct PPE component behaviors, including rapid contour variations near sources, zero-field limits at large distances, increased contour density near point charge sources in fluids, and higher-order singularities in shear stress around concentrated sources. These findings offer valuable insights into the physical mechanisms of PPE materials and expand their potential for innovative engineering applications.

关键词： Transversely isotropic materials Porous materials Piezoelectric materials Green's functions potential theory method

来源：评论

学校读者我要写书评

暂无评论

Analyzing point liquid loading effects on transversely isotropic poroelastic media using Green's function

引用

COMMUNICATIONS IN THEORETICAL PHYSICS 2025年第8期77卷 085001-085001页

Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot's theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi's theorem. Based on these general solutions and potential functions, we construct a Green's function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.

关键词： poroelasticity one-point loading Green's functions transversely isotropic materials potential theory method

来源：评论

学校读者我要写书评

暂无评论

Poroelasticity in infinite orthotropic materials with smooth interfaces via Green's functions

引用

ARCHIVE OF APPLIED MECHANICS 2025年第5期95卷 1-15页

作者： Tariq, Muzammal Hameed Pan, Li-Hua Zhou, Yue-Ting Ren, Jingli Dang, Huayang Tongji Univ Sch Aerosp Engn & Appl Mech Shanghai 200092 Peoples R China AECC Hunan Aviat Powerplant Res Inst Zhuzhou 412002 Peoples R China Shanghai Inst Aircraft Mech & Control 100 Zhangwu Rd Shanghai 200092 Peoples R China Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China Zhengzhou Univ Sch Mech & Engn Sci Zhengzhou 450001 Peoples R China

Green's functions are essential analytical tools in physics, providing key insights into the behavior of complex multiphase systems. This study examines poroelastic effects in infinite orthotropic materials with smooth contact interfaces using Green's functions, which play a significant role in flotation mattresses and rock-soil systems. By employing strict differential operator theory and potential theory, we present compact mono-harmonic general solutions to the governing equations that satisfy sixth-order homogeneous partial differential equations. Based on the obtained compact general solution, the 2D fundamental solution for a steady line fluid source in an infinite orthotropic poroelastic plane with smooth interfaces is derived using six newly introduced harmonic ***, ensuring their ease of use in practical applications. Numerical simulations, presented through non-dimensional contours and spatial visualization, reveal elliptical behavior, high-density levels near the fluid source, decay at a distance, higher-order singularities, zero-common tangents, and adherence to interface continuity conditions.

关键词： Two-phase Orthotropic materials General solution Poroelasticity Green's functions potential theory method

来源：评论

学校读者我要写书评

暂无评论

Three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure in thermal environment

引用

MATHEMATICS AND MECHANICS OF SOLIDS 2023年第9期28卷 2057-2074页

作者： Yang, Licai Nucl Power Inst China Sci & Technol Reactor Syst Design Technol Lab Chengdu Peoples R China Nucl Power Inst China Sci & Technol Reactor Syst Design Technol Lab Chengdu 610213 Peoples R China

The novelty of this paper is to propose exact three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure for the first time, in which uniform heat flux flowing from rigid structure into the half infinite body is considered. Using recent general solutions expressed by four harmonic functions and extending potential theory method to consider heat effect, the governing integral equations are first derived. Then, the equations are analytically solved and displacement, stress, and temperature field components expressed by elementary functions are obtained. To validate the presented solutions, the correctness of the solutions is exactly examined, and normal contact displacement and stress without heat effect are compared with those in literatures. Furthermore, a numerical example which is the stainless steel thermo-elastic body pressed by a displacement restrictor is studied. Displacement, stress, and temperature distributions are analyzed, and the influence of heat flux on the pressed depth is also discussed in detail. The analytical solutions presented in this paper are rather important in engineering practice and can provide a basis for indentation analysis, displacement restrictor design, foundation settlement calculation, and so on.

关键词： Three-dimensional analytical solutions half infinite thermo-elastic body potential theory method elementary functions heat flux

来源：评论

学校读者我要写书评

暂无评论

Three-dimensional thermal-mechanical analytical solutions for the half-space pressed by an inclined rigid cylindrical structure

引用

JOURNAL OF THERMAL STRESSES 2023年第10期46卷 1045-1065页

作者： Yang, Licai Qiu, Tian Zhang, Shanglin Nucl Power Inst China Sci & Technol Reactor Syst Design Technol Lab Chengdu 610213 Sichuang Peoples R China

Three-dimensional thermal-mechanical analytical solutions to the elastic half-space pressed by an inclined rigid cylindrical structure are presented in this article for the first time, based on the recent thermo-elastic general solutions in terms of harmonic functions and potential theory method. The obtained solutions are proved to be closed. The adequate validations are provided by comparing contact displacement and contact pressure on the contact plane from the presented solutions with those without heat effect in literatures. The geometric distribution of temperature on the contact region is also in accordance with that by previous researcher for the composite material under uniform heat flux. In addition, for the purpose of engineering application, a numerical example which is thermal contact problem between an inclined rigid circular displacement restrictor and elastic half-space is given, and the distributions of key field variables and effects of heat flux on contact pressure and normal displacement are discussed in detail.

关键词： An inclined rigid cylindrical structure elastic half-space potential theory method thermal-mechanical three-dimensional

来源：评论

学校读者我要写书评

暂无评论

Green's functions for infinite orthotropic, hygro-electro-magneto-thermoelastic materials

引用

ARCHIVE OF APPLIED MECHANICS 2022年第11期92卷 3325-3342页

The current study is attempted to explore the general solution for the plane problem of an orthotropic hygro-electro-magneto-thermoelastic material (HEMTM). A complete general solution is accomplished by the aid of operator theory and superposition principle, which satisfies twelfth order partial differential equation. Moreover, the obtained general solution is simplified in terms of six harmonic functions and is helpful for boundary value problem of HEMTM. As an application, the fundamental solution for a steady point moisture source combined with heat source in an infinite HEMTM is derived using the general solution. Consequently, exact and complete solutions in terms of elementary functions are obtained, which can serve as a benchmark for various kinds of numerical codes and approximate solutions. Along with this, numerical simulations are conducted using the general solution and graphically illustrated.

关键词： Hygro-electro-magneto-thermoelasticity General solution Orthotropic Two-dimensional potential theory method

来源：评论

学校读者我要写书评

暂无评论

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

引用

MATHEMATICS AND MECHANICS OF SOLIDS 2022年第7期27卷 1233-1254页

作者： Liu, Yuwei Tang, Xuesong Duan, Peiliang Wang, Tao Li, Peidong Southwestern Univ Finance & Econ Sch Accounting Chengdu Peoples R China Chengdu Univ Business Sch Chengdu Peoples R China Gaosheng Oil Prod Petrochina Liaohe Oilfield Co Panjing Peoples R China Chengdu Surveying Geotech Res Inst Co Ltd MCC Chengdu Peoples R China Sichuan Univ Dept Mech & Engn Chengdu 610065 Peoples R China

In this paper, an analytical solution is developed for the problem of an infinite 1D hexagonal piezoelectric quasi-crystal medium weakened by an elliptical crack and subjected to mixed loads on the crack surfaces. The mixed loads comprise the phonon pressure, phason pressure, electric displacement, and temperature increment, and the crack surfaces can be electrically permeable or impermeable. Based on a general solution, combined with the generalized potential theory, the steady-state 3D thermo-electro-elastic field variables in the quasi-crystal are obtained in terms of elliptic integral functions and elementary functions. Several important physical quantities on the cracked plane, such as the generalized crack surface displacements, normal stresses, and stress intensity factors, are derived in closed forms. An illustrative numerical calculation verifies the presented analytical solution and shows the distribution of the 3D thermo-electro-elastic field. It is indicated that the influence of the phason field on the result is pronounced, especially for the electric field variables, and the electric permeability of crack surfaces has a significant effect on the electric displacement intensity factor at the crack tip.

关键词： 1D hexagonal piezoelectric quasi-crystal elliptical crack thermo-electro-elastic field analytical solution potential theory method

来源：评论

学校读者我要写书评

暂无评论

General solution and Green?s function for fluid-saturated infinite and semi-infinite orthotropic poro-thermoelastic materials

引用

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2023年 97卷

作者： Tariq, Muzammal Hameed Ren, Jingli Zhengzhou Univ Henan Acad Big Data Sch Math & Stat Zhengzhou 450001 Peoples R China

In this study, two-dimensional (2D) steady-state general solution and Green's function for orthotropic materials under the influence of poro-thermoelasticity (PTE) are investigated. Using the superposition principle and operator theory, the complete general solution of corresponding governing equations is calculated and stated in terms of harmonic functions. Based on these compact general solutions, the 2D Green's function for a steady line fluid source and line heat source in the interior of an infinite orthotropic PTE plane and on the surface of a semi-infinite orthotropic PTE plane is presented. Consequently, eight newly implemented harmonic functions with undetermined constants are obtained. The equilibrium, boundary, and continuous conditions are used to obtain undetermined constants, and the corresponding coupled field is obtained by inserting these harmonic functions into the general solution. All coupled field's components are described in terms of elementary functions, which can be used as the benchmarks for various numerical codes and approximate solutions.

关键词： Green?s function General solution Orthotropic materials Poro-thermoelasticity potential theory method

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：