THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＮＯＮＬＩＮＥＡＲＡＮＡＬＹＳＩＳＦＯＲＰＥＲＦＯＲＡＴＥＤＴＨＩＮＰＬＡＴＥＳＣｈｅｎｇＣｈａｎｇｉｕｎ（程昌钧）；ＹａｎｇＸｉａｏ...     

Region-wise variational principles and generalized variational principles on large strain for consolidation theory

Introduction Thedeformationofsaturatedsoftclayisoneofimportantquestionsingeotechnical engineering.Thenotablecharacteristicisthatthedegreeofitsstrainisgenerallylargerthan10percent.Oneofthecauses[1],Whichleadtoaquantitativedifferencebetweenthe numericalsimu…     

The generalized variational principles with their applications in structural analysis

This paper will chseuss the generalized variational prinetples.which the established bythe methed of undetermined multipliers in structures.and analys the statiedllyindeterminate truss.in which these principles will be used.At the same time we bring asymmetrical matrix and give speeitie sohution.thus all the internal forees of structures maybe found.     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

电磁弹性动力学初边值问题12类变量广义变分原理

基于Yao建立的电磁弹性固体广义变分原理,运用关于非传统Hamilton型广义变分原理的方法,建立了电磁弹性动力学初边值问题的12类变量广义变分原理,可反映该问题的全部特征,其独立变分变量为该问题的全部变量,即位移、速度、动量、应变、应力、电位移、磁感应强度、电场强度、磁场强度、电标量势、磁标量势和磁矢量势.本文建立的...     

The variational principles and application of nonlinear numerical manifold method

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｉｎｉｔｅｃｏｖｅｒｔｅｃｈｎｉｑｕｅｓ,ｓｉｍｉｌａｒｔｏｔｈｅｃｏｎｃｅｐｔｉｏｎｏｆｆｉｎｉｔｅｃｏｖｅｒｕｓｅｄｉｎｍａｎｉｆｏｌｄａｎａｌｙｓｉｓｏｆｍｏｄｅｒｎｍａｔｈｅｍａｔｉｃｓ,ａｒｅｉｎｔｒｏｄｕｃｅｄｉｎｔｏＮｕｍｅｒｉｃａｌＭａｎｉｆｏｌｄｍｅｔｈｏｄ (ＮＭＭ)ａｎｄｔｈｅｆｉｎｉｔｅｃｏｖｅｒｓｃｏｎｓｉｓｔｏｆｍａｔｈｅｍａｔｉｃａｌｃｏｖｅｒｓａｎｄｐｈｙｓｉｃａｌｃｏｖｅｒｓｗｈｉｃｈｃａｎｂｅｓｅｐａｒａｔｅｄ .ＴｈｅＮＭＭｉｓｃｏ…     

Generalized variational principles on nonlinear theory of elasticity with finite displacements

Two generalized variational principles on nonlinear theory of elasticity with finitedisplacements in which the σ_(ij),e_(i j)and u_i are all three kinds of independent functionsare suggested in this paper.It isproved that these two generalized variational principles areequivalent to each other if the stress-strain relation is satisfied as constraint.Some specialcases,i.e.generalized variational principles on nonlinear theory of elasticity with smalldeformation,on linear theory with finite deformation and on linear theory with smalldeformation together with the corresponding equivalent theorems are also obtained.All ofthem are related to the three kinds of independent variables.     

Generalized variational principles of the viscoelastic body with voids and their applications

From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.     

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

ＦｕＢａｏｌｉａｎ（付宝连）（ＲｅｃｅｉｖｅｄＮｏｖ．２２，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩ...     

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.     

On the variational principles in linear elastodynamics

A new approach is proposed for the systematic derivation of varïous variational principles in linear elastodynamics. Based on an important integral relation in terms of convolutions given by the authors, the new approach can be used to derive the complementary functionals for the five-field, four-field, three-field, two-field and one-field variational principles more simply and directly. Furthermore, with this approach, it is possible not only to derive the variational principles given by Herrera and Bielak, Oden and Reddy, but also to develop new more general variational principles. And the intrinsic relationship among various principles can be explained clearly.     

Generalized variational principle on nonlinear theory of naturally curved and twisted closed thin-walled composite beams

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｔｉｃａｎｄｄｙｎａｍｉｃｎｏｎｌｉｎｅａｒａｎａｌｙｓｉｓｉｎｔｈｅｎａｔｕｒａｌｌｙｃｕｒｖｅｄａｎｄｔｗｉｓｔｅｄｃｌｏｓｅｄｔｈｉｎ＿ｗａｌｌｅｄｓｌｅｎｄｅｒｂｅａｍｓ(ａｂｂｒｅｖｃｕｒｖｅｄａｎｄｔｗｉｓｔｅｄｔｈｉｎ＿ｗａｌｌｅｄｃｏｍｐｏｓｉｔｅｂｅａｍｓ)ｏｆｔｈｅｆｉｂｒｅ＿ｒｅｉｎｆｏｒｃｅｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｓｉｓｃｏｍｍｏｎｌｙａｎｄｍａｉｎｌｙａｐｐｌｉｅｄｉｎｃｈｅｍｉｃａｌｉｎｄｕｓｔｒｙａｎｄａｅｒｏｎａｕｔｉ…     

Generalized sub-region mixed and hybrid variational principlesin nonlinear elastodynamics

In this paper, the Hu-Washizu generalized variational principle isextended to nonlinear elastodynamics with five independent fields. The twokinds of framework of functional, the potential energy and complementaryenergy expressions containing the subsidiary conditions with Lagrangemultipliers are suggested. According to the principle of stationaryfunctional, we have the governing equations and Lagrange multipliersdetermened by the results of variation. The generalized sub-region mixed andhybrid variational principle in nonlinear elastodynamics is presented.Supported by National Natural ScienceFoundation of China.     

GURTIN-TYPE REGION-WISE VARIATIONAL PRINCIPLES FOR THERMOPIEZOELECTRIC ELASTODYNAMICS

IntroductionThemethodofconvolution[1- 3]canbeusedinthestudyofpiezoelectricmaterial.Piezoelectricmaterialisoneoftheimportantsmartmaterials,usedinnovelsmartstructure .ThedynamictheoryforthermopiezoelectricelastomediawassearchedbyNowacki[4 ,5 ],Chandrasekharaiah[6 ]andIesan[7].However,region_wisevariationalprinciplesinlinearthermopiezoelectricelastodynamicshavebeennotestablishedsystematically .AlthoughLuoenandKuangJun_shang[8]havedevelopedsimplifiedGurtin_typevariationalprinciplesinlinearther…     

Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures

According to the basic idea of classical yin-yang complementarity and modem dual-complementarity,in a simple and unified new way proposed by Luo,the unconven- tional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically,which can fully charac- terize the initial-boundary-value problem of this kind of dynamics.An important in- tegral relation is made,which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechan- ics.Based on such relationship,it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures,but also to derive systematically the complementary functionais for five-field,four-field,three-field and two-field unconventional Hamilton-type variational principles,and the functional for the unconventional Hamilton-type variational principle in phase space and the poten- tial energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the general- ized Legendre transformation given in this paper.Furthermore,the intrinsic relationship among various principles can be explained clearly with this approach.     

The variational principles of coupled systems in photoelasticity

ＴＨＥＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＣＯＵＰＬＥＤＳＹＳＴＥＭＳＩＮＰＨＯＴＯＥＬＡＳＴＩＣＩＴＹＦｕＢａｏ－ｌｉａｎ（付宝连）（ＹａｎｓｈａｎＵｎｉｖｅｒｓｉｔｙ,Ｑｉｎｈｕａｎｇｄａｏ）（ＲｅｃｅｉｖｅｄＮｏｖ．８,１９８９,Ｃｏ...     

用广义变分原理求解多节点双模量静不定桁架

在外载荷作用下的多节点双模量静不定桁架平衡问题,是任意有限多个自变量的多元函数在任意有限多个约束条件下的极值问题,采用广义变分原理可以方便求解多节点双模量静不定桁架内力．通过求解多节点双模量静不定桁架内力的几个算例,阐述广义变分原理在计算多节点双模量静不定桁架内力中的应用．研究结果表明：采用广义变分原理求解多节点双模量静不定桁架内力的通用性较强,所求的结果是精确解析解．采用广义变分原理求解多节点双模量静不定桁架内力的方法不但克服了常规方法需利用几何关系建立协调方程的缺陷,且具有力学概念清晰直观、计算过程简便、便于工程设计人员在实际中掌握和计算等优点．     

some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics

From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5], [17]-[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variati     

Generalized variational inequalities and generalized quasi-variational inequalities

Under much weaker hypotheses and in a more general setting some existence theorems of solutions to generalized variational inequalities,generalized quasi-varia-tional inequalities and minimax inequalities are established.The results presented in this paper generalize the corresponding results of[3—13]to the noncompact case,thus improving these results.