COMPARISON OF THE CALCULATIONS OF THREE-CONVOLUTION CIRCULAR ARC CORRUGATED DIAPHRAGMS BY TOROIDAL SHELL THEORY AND BY ORTHOGONAL ANISOTROPY PLATE THEORY

The calculation of elastic deformations of corrugated diaphragms was given by orthogonal anisotropy plate theory, and its result agrees with the experimental results. But it has never been discussed seriously how the number and form of convolutions affect the elastic deformations and stress distributions of anisotropyplate. As a result, adaptable limits of orthogonal anisotropy plate theory cannot be indicated when it is used to calculate diaphragms. It is said that the theory is fairly good for calculating elastic deformations of the diaphragms which have more convolutions. It is also said that the error in calculating stresses is rather large. This paper, by using the toroidal shell theory, presents the calculation of deformationsand stresses of three-convolution circular are corrugated diaphragms both symmetrical and unsymmetrical, compares its result with that of the orthogonal anisotropy plate theory and gives definite adaptable limits of the latter theory.     

THE EXTREMITY LAWS OF HYDRO-THERMODYNAMICS

This paper presents the law of maximum rate of energy dissipa-tion in hydrodynamics and also in general continuum dynamicsas an addition to the classical conservation laws expressed inthe equation of continuity and the equations of motion.Thecorollary of the law is B(?)langer-B(?)ss theorem of minimum reser-ved specific energy in applied hydraulics.The mechanical energy dissipated is transformed into heatreserved in the substance.The rate of energy dissipation ata time at a given temperature gives rise to the increase in en-tropy production.Hence the maximum rate of energy dissipationsuggests itself the idea of reformulation of the second law ofthermodynamics that the rate of entropy production in mech-anical motion is always the maximum possible.The proposed extremity law in continuum dynamics has beenderived from the variational principle and the reformulatedsecond law of thermodynamics analyzed microscopically in thepaper.The two laws together form the extremity laws of hydro-thermodynamics.     

ANALYSIS OF ADHESIVE LAP JOINT

This paper is to solve the interlaminar stresses of adhesive lap joint by the energymethod without considering the adhesive layer. The joint is made of two identical narrowplates.Two cases are discussed:one is for the isotropic material and the other is fororthotropic material.Because of the different materials forming the joint,the length ofdistribution and the magnitude of the interlaminar stresses for the two cases will be verydifferent.     

THF GENERAL VARIATIONAL PRINCIPLE OF THE CANTILEVER BEAM OF CIRCULAR CROSS SECTION INCLUDING TRANSYERSE SHEAR DEFORIIATION

In this paper we derive the approximate theory On the straight cantilever beam of a same circular cross section including transverse shear deformation, using the general variational principle with two class variates, and we present the expression with two class variates containing two general displacement, of general complementary energy, corresponding with the theory.     

THE SEPARATION OF LARGE VORTEXES AND THE CLOSED EQUATIONS OF TURBULENCE MODEL

This paper presents a new kind of average for the locally-generated large vortexes sothat the physical quantities of the locally-generated large vortexes and the external largevoriexes can be rigorously separated from the equations for the large vortexes proposed in aprevlous paper.To the equations the two kinds of large vertexes.some auxiliaryrelations are introduced,and the value of the length-scale l_N of energy dissipation of theexternal large vortexes may be determined according to the actual circumstances of thedisturbance of external sources.Thus,the resulting equations of second moments ofturbulent velocity fluctuations for the two kinds of large vortexes can be made closed.Meanwhile,the corresponding coefficients of diffusion in the previous paper areimproved.Finally,a closed set of numerically-solvable equations of turbulence model areobtained.     

SOME APPLICATIONS OF THE SINGULAR PERTURBATION METHOD TO THE BENDING PROBLEMS OF THIN PLATES AND SHELLS

This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.     

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variational principle,a sub-region mixed ver- sion of the newly-developed semi-analytical‘finite element method of lines’(FEMOL)is pro- posed in this paper for accurate and efficient computation of stress intensity factors(SIFs)of two-dimensional notches/cracks.The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used,with the sought SIFs being among the unknown coefficients.The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements.A mixed system of ordinary differential equations(ODEs) and al- gebraic equations is derived via the sub-region generalized variational principle.A singularity removal technique that eliminates the stress parameters from the mixed equation system even- tually yields a standard FEMOL ODE system,the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver.A number of numerical examples,including bi-material notches/cracks in anti-plane and plane elasticity,are given to show the generally excellent performance of the proposed method.     

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.     

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to bt, cubic polynomials and to satLyfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical.shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.     

A SIMPLIFIED METHOD FOR THE CONSTRUCTION OF THE CUBIC SPLINE FUNCTION

This paper gives a simplified method for the construction of the cubic spline function.discusses the related problems, and at last, presents the treatment for its different cases.     

APPLICATIONS 0F THE RECIPROCAL THEOREM TO SOLVING THE EQUATIONS OF THE DEFLECTION SURFACE OF THE RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS

This paper points out that on certain condition the reciprocaltheorem is equivalent to the superposition principle of displacements.On the basis of[6],applications of the reciprocal theorem are fur-ther extended;a convenient.general and new method for solving theequations of deflection surface of the rectangular plates and thestraight beams with various edge conditions under various loads is pre-sented.     

A METHOD OF FINDING THE PRINCIPAL MODES OF NONLINEAR VIBRATION SYSTEMS AND THEIR STABILITIES

This paper presents a new method of finding the principal modes of nonlinear vibrationsystems,by means of which the problem of finding principal modes of nonlinear systems istransferred to the problem of finding real roots of a set of algebraic equations.The methodis applicable to various kinds of nonlinear vibration systems with many degrees of freedom,and is simple in calculation.The paper presents another new method of analyzing thestabilities of principal modes of nonlinear systems.     

THE DISTRIBUTION OF THE SPECIFIC PRESSURE IN ROLLING STRIPS

The principle of the distribution of the specific pressure in rol-ling strips is used not only for calculating the total rolling pres-sure but also for providing the basis in calculating the widening andin designing the rational roll profile.Hitherto,the results of an-alysis on this subject in the references are expressed as a functionof one dimension,and they cannot reflect the variation of the speci-fic pressure along the width of the contact surface.This paper dealswith the two-dimensional expression of the principle.of the distribu-tion of the specific pressure with the help of the calculus of varia-tions.     

ON THE LAW OF ENERGY CONSERVATION IN THE CLASSICAL ELECTRODYNAMICS OF DEFORMABLE MEDIA——A GENERALIZATION OF THE POYNTING THEOREM

This paper establishes the generalized Poynting theorem for the electrodynamics of deformable media with a view to shedding some light on the detailed mechanism of energy transfer between the electromagnetic field and the deformable media. Global field equations are chosen as the starting point and specialized forms of the theorem are derived based on the special postulates for the electromagnetic body force.     

THE METHOD OF TRANSFORMATION OF THE BOUNDARIES FOR STRUCTURE THE ADMISSIBLE DISPLACEMENTS

In this paper the method of transformation of the boundaries for structure theadmissible displacements with various boundary conditions is presented What is called themethod of transformation of the boundaries is that. first we transform the actual systeminto the basic system and additional boundary forces and displacements on the basis of thesuperposition principle, then apply variational principles to the basic system,finally find thepermissible displacement of the actual system by means of the method of transformation ofthe series.In this paper, we also give mixed energy prinapies under Variation of boundaryconditions. The mixed energy principles as the potential and complementary energyprinciples under variation of boundary conditions are all the chief theoretical fundamentalof the method of transformation of the boundaries.Applying the method of transformation of the boundaries. we form the permissibledisplacements of rectangular plates of plane stress and bending problems with various edgeconditio     

THE UNSYMMETRICAL BENDING OF CANTILEVER RECTANGULAR PLATES

This paper discusses the problems of the unsymmetrical bending of cantileverrectangular plates under various loads by the energy method.We illustrate numerouscalculating examples such as the plates which are subjected by the concentrated forces orconcentrated couples unsymmetrically on free sides and corner points and by a uniformly ornonuniformly distributed loads unsymmetrically on free edges and so forth.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

THE VALIDITY OF THE MODIFIED MORI-TANAKA METHOD FOR COMPOSITES WITH SLIGHTLY WEAKENED INTERFACE

This paper presents a direct Mori-Tanaka approach to calculate the effective moduli ofparticle-reinforced composites and fiber-reinforced composites with spring like imperfect interfaces.Bya comparison between these results and those obtained from the approximate Mori-Tanaka method de-veloped by Qu for composites with slightly weakened interface,the validity of the Qu's method is re-vealed.