THE RECIPROCAL THEOREM AND LINEAR ELASTIC VARIATIONAL PRINCIPLES

In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.     

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS

In this paper, the variational principles of hgdrodynamic problems for the incompressibleand compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.     

ON VARIOUS VARIATIONAL PRINCIPLES IN NONLINEAR THEORY OF ELASTICITY

In the present paper functionals for the various possiblemain variational principles in the nonlinear theory of e-lasticity are derived from the“full energy principle” andseveral of them are not found yet in the literatures avail-able. Through the derivation of this paper we suggest aconjecture on the nonexistence of the eleventh and thesixth classes for the variational principles in Table 6.1of H. C. Hu’s monograph [1].     

NAVIER SOLUTION FOR THE ELASTIC EQUILIBRIUM PROBLEMS OF RECTANGULAR THIN PLATES WITH VARIABLE THICKNESS IN LINEAR AND NONLINEAR THEORIES

This paper discusses the elastic equilibrium problems of rectangular thin plates ofvarying thickness and simply supported on all four sides by linear and nonlinear theory.using the Navier method to seek an approach to the problem,and illustrates the solutionwith two examples.In conclusion,mention is made of scope of application and theconvergency of the solution.     

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 FREE ENERGY AND VARIATIONAL THEOREN OF ELASTIC PROBLEM IN THERMAL SHOCK

In some investigations on variational principle for cou-pled thermoelastic problems,the free energy φ(e_(ij),θ) ,Wherethe state variables are elastic strain e_(ij) and temperatureincrement θ,is expressed asφ(e_(ij),θ)=λ/2e_(kk)e(ij) μe_(ki)e_(kj)-γe_(kk)θ-c/2ρθ~2/T_o (0.1)This expression is employed only under the condition of|θ|≤T_o (absolute temperature of reference)But the value of temperature increment is great, evengreater than T_o in thermal shock. And the material pro-perties (λ,μ,γ,c,etc.) will not remain constant,theyvary with θ.The expression of free energy for this con-dition is derived in this paper. Equation (0.1) is itsspecial case.Euler’s equations Will be nonlinear While this expres-sion of free energy has been introduced into variationaltheorem. In order to linearise, the time interval of ther-mal shock is divided into a number of time elements △t_k(△t_k=t_k-t_(k-1),k=1,2,…,n),Which are so small that the tempera-ture increment θ_k within it is very small,too.Thus,t     

VARIATIONAL METHODS FOR THE PROBLEMS OF NONCONSERVATIVE FORCE FIELDS IN THE MICROPOLAR ELASTODYNAMICS

Based on the properties of the convolution and the convolute commutation, somequasi-variational principles for the problems of nonconservative force field in themicropolar elastodynamics are given and verified in this paper. The theorem given in thispaper can be applied to the theories of the nonlocal elastic mediums and the nonlocalmicropolar elastic mediums.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅰ)—MICROPOLAR CONTINUA

Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete. Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: Dupai Tian-min (1931≈)     

THE LARGE DEFLECTION ON PROBLEM OF CIRCULAR PLATE ON ELASTIC FOUNDATION AND IN CONJUNCTION WITH LINEAR ELASTIC STRUCTURE

This paper deals with the axisymmetrical deformation of the circular plate in largedeflection,which is on elastic foundation and in conjunction with a certain linear elasticstructure.The governing integral equations are established by the method of mixedboundary condition I and the simplified form is given.The pertrubation method is used toobtain the solutions and an example of the composite structure made up of a circular plateand a cylindrical shell is presented.     

ON THE UNIFICATION OF THE HAMILTON PRINCIPLES IN NONHOLONOMIC SYSTEM AND IN HOLONOMIC SYSTEM

ＯＮＴＨＥＵＮＩＦＩＣＡＴＩＯＮＯＦＴＨＥＨＡＭＩＬＴＯＮＰＲＩＮＣＩＰＬＥＳＩＮＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＡＮＤＩＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭ（梁立孚）（韦扬）ＯＮＴＨＥＵＮＩＦＩＣＡＴＩＯＮＯＦＴＨＥＨＡＭＩＬＴＯＮＰＲＩＮＣＩＰＬ...     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅰ) —MICROPOLAR CONTINUA

IntroductionThemicropolarcontinuumtheoryisatypicalandwideapplicatedtheoryinthegeneralizedcontinuumtheoriesandwasgenerallyrecognizedlongago .Manymonographsandalargenumberofscientificpapersconcerningthisfieldarepublished .Wehaverestudiedtheexistingpolarcontinuumtheoriesandfoundthatsomebasicbalancelawsandprinciplesofthemareincompleteandthereexistsometheoreticaldefectswhichshouldberemoved .Forcontrastandclaritywenowlistthetraditionalbasicbalancelawsandequationsformicropolarcontinuumtheoryasfollows…     

THE NEW CRITERIA OF ELASTIC AND FATIGUE FAILURE IN THE COMPONENT OF COMPLEX STRESS STATES

In this paper, a total criterion on elastic and fatigue failure in complex stress, that is, octahedral stress strength theory on dynamic and static states on the basis of studying modern and classic strength theories. At the same time, an analysis of an independent and fairly comprehensive theoretical system is set up. It gives generalized failure factor by 36 materials and computative theory of the 11 states of complex stresses on a point, and derives the operator equation on generalized allowable strength and a computative method for a total equation can be applied to dynamic and static states. It is illustrated that the method has a good exactness through computation of eight examples of engineering. Therefore, the author suggests applying it to engineering widely.     

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

ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＮＯＮＬＩＮＥＡＲＡＮＡＬＹＳＩＳＦＯＲＰＥＲＦＯＲＡＴＥＤＴＨＩＮＰＬＡＴＥＳＣｈｅｎｇＣｈａｎｇｉｕｎ（程昌钧）；ＹａｎｇＸｉａｏ...     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS(Ⅲ)——RE-DISCUSS THE LINEAR THEORY OF NONLOCAL ELASTICITY

In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal consitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given. Foundation item: the Natural Science Foundation of Jiangsu Province, China (BK97063)     

DIFFRACTION OF ELASTIC WAVES IN THE PLANE MULTIPLY-CONNECTED REGION AND DYNAMIC STRESS CONCENTRATION

This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions.The complete function series whichapproach the solution of the problem and general expressions for boundary conditions aregiven.Then the problem is reduced to the solution to infinite series of algebraic equationsand the solution can be directly obtained by using electronic computer.In particular,for thecase of weak interaction,an asymptotic method is presented here,by which the problem of pwaves diffracted by a circular cavities is discussed in detail.Based on the solution of thediffracted wave field the general formulas for calculating stress concentrationfactor for a cavity of arbitrary shape in multiply-connected region are given.     

NEW POINTSOF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS( Ⅲ) ——RE_DISCUSS THE LINEAR THEORY OF NONLOCAL ELASTICITY

Ｔｈｅｌｉｎｅａｒｔｈｅｏｒｙｏｆｎｏｎｌｏｃａｌｅｌａｓｔｉｃｉｔｙｈａｓｂｅｅｎａｐｐｌｉｅｄｔｏｓｏｍｅｐｒｏｂｌｅｍｓｓｕｃｈａｓｆｒａｃｔｕｒｅ,ｄｉｓｌｏｃａｔｉｏｎａｎｄｗａｖｅｐｒｏｐａｇａｔｉｏｎ［１］．Ｉｔｉｓｕｓｅｄｔｏｓｏｌｖｅｍａｎｙｐｒｏｂｌｅｍｓｗｈｉｃｈａｒｅｎｏｔｅｘｐｌａｉｎｅｄｂｙｔｈｅｃｌａｓｓｉｃａｌｍｅｃｈａｎｉｃｓ．Ｉｔｉｓｐｏｉｎｔｅｄｏｕｔｅａｒｌｉｅｒ［２］,ｈｏｗｅｖｅｒ,ｓｏｍｅｉｍｐｏｒｔａｎｔｎｏｎｌｏｃａｌｐｒｏｐｅｒｔｉｅｓｉｎｔｈ…     

THE SOLUTION OF DEFLECTION OF ELASTIC THIN PLATE BY THE JOINT ACTION OF DYNAMICAL LATERAL PRESSURE, FORCE IN CENTRAL SURFACE AND EXTERNAL FIELD ON THE ELASTIC BASE

In this paper the Euler equation of the deflection of elastic thin plate is reduced to the equation with Schrǒdinger form by the principle of quantum electro-dynamics.Then we can obtain the general solution of deflection of elastic thin bending plate by the joint action of dynamical lateral pressure, force in central surface and external field on the elastic base.     

THE METHOD OF SOLVING AXISMMETRIC PROBLEMS IN ELASTIC SPACE BY COMPLEX FUNCTION AND SOME EXAMPLES

This paper proves Love's stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variates reasonably, and deduces the expressions of the components of stress displacements and boundary conditions in complex function. To present the feasibility of the method here and examining the truth of the formulae founded in this paper, the problem of circular shaft with globular cavity pressed on the side and pulled at the ends is solved by using power series and the result is the same as that solved by other methods. In the end, the problem of a cone sheared by uniform shear stress on the sideface is solved, and the solution of a cone acted on by gravity is given by converting constant body forces into surface forces.     

THEOREMS ON THE LIMIT ANALYSIS DEALING WITH THE YIELD CONDITION EXPRESSED BY THE SUM OF THE HOMOGENEOUS LINEAR FORM OF STRESS TENSOR AND THE HOMCGENEOUS QUADRATIC FORM OF STRESS TENSOR

In this paper a generelized variational principle on the limitanalysis dealing With the yield condition expressed by thesum of the homogeneous linear form of stress tensor and thehomogeneous quadratic form of stress tensor is suggested.Thisvariational principle can be applied to the limit analgsis inrock mechanics and it takes the situation.in which the yieldcondition is expressed by the homogeneous linear form of stresstensor or the homogeneous quadrdtic form of stress tensor.asits special case.     

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

ＴＨＥＧＥＮＥＲＡＴＩＯＮＯＦＮＯＮ－ＬＩＮＥＡＲＳＴＩＦＦＮＥＳＳＭＡＴＲＩＸＯＦＴＲＩＡＮＧＬＥＥＬＥＭＥＮＴＷＨＥＮＣＯＮＳＩＤＥＲＩＮＧＢＯＴＨＴＨＥＢＥＮＤＩＮＧＡＮＤＩＮ－ＰＬＡＮＥＭＥＭＢＲＡＮＥＦＯＲＣＥＳｚｈａｎｇＪｉａｎ－ｈａｉ（...