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Coupled thermoelastic theory and associated variational principles based on decomposition of internal energy

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Acta Mechanica Sinica 2020年第1期36卷 107-115页

作者： Jia-Hong Zheng Zheng Zhong Cong-Ying Jiang School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai200092China School of Science Harbin Institute of Technology(Shenzhen)Shenzhen518055GuangdongChina

A new framework of coupled thermoelasticity is constructed in this paper based on a decomposition of internal energy into free internal energy and dissipative energy.Fundamental equations(i.***.divergence and gradient equations,constitutive equations including evolving laws)along with proper boundary conditions are all included in this framework,from which two novel dual-complementary variational principles with explicit functionals are proposed.Unlike the conventional thermoelastic theory,the proposed variational principles for thermoelasticity are established without the approximate assumption of small temperature changes.To verify the usefulness of the proposed variational principles in simulating coupled thermoelastic problems,a coupled thermoelastic example is numerically implemented.

关键词： Coupled thermoelasticity Thermodynamics Dissipation variational principle

Study on interface failure of shape memory alloy(SMA)reinforced smart structure with damages

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Acta Mechanica Sinica 2005年第3期21卷 286-293页

作者： Zili Hu Ke Xiong Xinwei Wang The Aeronautical Science Key Laboratory for Smart Materials and Structures Nanjing University of Aeronautics and Astronautics. Nanjing 210016 China

Shape memory alloy （SMA） reinforced smart structure can be used to make structural shape and strength selfadapted and structural damage self-restrained. Although SMA smart structures without damages were extensively studied, researches on SMA smart structures with damages have rarely been reported thus far. In this paper, thermo-mechanical behaviors of SMA fiber reinforced smart structures with damages are analyzed through a shear lag model and the variational principle, Mathematical expressions of the meso-displacement field and the stress-strain field of a typical element with damages are obtained, and a failure criterion for interface failure between SMA fibers and matrix is established, which is applied to an example. Results presented herein may provide a theoretical foundation for further studies on integrity of SMA smart structures.

关键词： Smart structures Damages SMA Failure Meso-mechanics analysis variational principle

Neumann＇s method for boundary problems of thin elastic shells

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Applied Mathematics and Mechanics(English Edition) 2017年第4期38卷 543-556页

作者： Y. S. NEUSTADT Department of Civil Engineering Samara State Architectural and Building University Samara 443001 Russia

The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.

关键词： boundary problem thin elastic shell theory Neumann＇s method variational principle Korn＇s inequality distribution embedding theorem Green tensor

Mechanical model of organ of Corti

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Applied Mathematics and Mechanics(English Edition) 2017年第6期38卷 867-876页

作者： Yiqiang CHEN Wenjuan YAO Shaofeng LIU Department of Civil Engineering Shanghai University

According to the vibration characteristics of the organ of Corti （OC）, seven hypotheses are made to simplify the structure of the model, and a mechanical OC model is established. Using the variational principle, a displacement analytical expression is solved under a certain pressure. The results are in good agreement with experimental data, showing the validity of the formula. Combined with the damage caused by noise in clinic, it is found that the hardening of outer hair cells and outer stereocilia can lead to loss of hearing and generation of threshold shift. In addition, the results show that high frequency resonance occurs at the bottom of the basilar membrane （BM）, and low frequency resonance occurs at the top of the BM. This confirms the frequency selective characteristics of the BM. Further, using this formula can avoid interference of the envi- ronment and the technical level of the test personnel, and can evaluate performance of the OC objectively.

关键词： organ of Corti （OC） variational principle hardening of outer hair cells（OHCs） hardening of outer stereocilia threshold shift

Elliptical Gaussian solitons in synthetic nonlocal nonliear media

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Chinese Physics B 2011年第5期20卷 272-279页

作者：程爽王奇葛丽娟施解龙丁海霞申明 Department of Physics Shanghai University

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a ＂double-self-focusing＂ synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality. Based on the variational approach, it obtains the approximately analytical solution of such Gaussian elliptical solitons. It also computes the stability of the solitons by numerical simulations.

关键词： elliptical Gaussian solitons nonlocal nonlinearity variational principle beam propagation method

THERMODYNAMIC variational APPROACH FOR CLIMB OF AN EDGE DISLOCATION

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Acta Mechanica Solida Sinica 2009年第5期22卷 426-435页

作者： A.C.F.Cocks Department of Engineering Science University of OxfordParks RoadOxfordOX1 3PJUK

A general thermodynamic variational approach is applied to study the force on an edge dislocation, which drives the dislocation to climb. Our attention is focused on the physical mechanism responsible for dislocation climb. A dislocation in a material element climbs as a result of vacancies diffusing into or out from the dislocation core, with the dislocation acting as a source or a sink for vacancy diffusion in the material element. The basic governing equations for dislocation climb and the climb forces on the dislocation are obtained naturally as a result of the present thermodynamic variational approach.

关键词： dislocation climb driving forces variational principle

THE STATIONARY VALUE PROPERTY OF HAMILTON'S principle IN NON-HOLONOMIC SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 1997年第12期18卷 0-0,0-0+0-0+0-0页

作者：梁立孚梁忠宏石志飞 Harbin Engineering University Harbin P. R. China Harbin Institute of Technology Harbin P. R. China

This paper proves that Hanlilton's prmciple of both using the Appell-Chetaevcondition and not using the Appell-CHETAEV conditiion is the variational principle of stationary action.The relevant problems are discussed

关键词： variational principle non-holonomic system stationary action,analytical dynamics

EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT VARIABLES FOR PLANE ELASTICITY PROBLEMS

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Applied Mathematics and Mechanics(English Edition) 2003年第12期24卷 1390-1397页

作者：张耀明温卫东张作泉孙焕纯吕和祥 College of Energy & Power Engineering Nanjing University of Aeronautics and Astronautics School of Mathematics and Physics Northern Jiaotong Institute Department of Mechanics Dalian University of Technology

The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle.Based on this,the equivalent boundary integral equations(EBIE) with direct variables,which are equivalent to the original boundary value problem,were deduced rigorously.The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.

关键词： variational principle exterior problem equivalent boundary integral equation (EBIE)

A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

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Computers, Materials & Continua 2019年第4期59卷 31-55页

作者： Timon Rabczuk Huilong Ren Xiaoying Zhuang Division of Computational Mechanics Ton Duc Thang UniversityHo Chi Minh CityViet Nam Faculty of Civil Engineering Ton Duc Thang UniversityHo Chi Minh CityViet Nam Institute of Structural Mechanics Bauhaus-University Weimar99423 WeimarGermany Institute of Continuum Mechanics Leibniz University HannoverHannoverGermany State Key Laboratory of Disaster Reduction in Civil Engineering College of Civil EngineeringTongji UniversityShanghai200092China

A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.

关键词： Nonlocal operator method variational principle Nonlocal operators Hourglass mode