Effect of Temperature Sensitivity and Inelastic Behavior of Phase Materials on the Bearing Capacity of Plane Structures with Uniformly Stressed Reinforcement

An inelastic problem of uniformly stressed reinforcement of plane temperature-sensitive composite structures is formulated. Analytical solutions are obtained for the thermoelastic and inelastic cases. On the basis of these solutions, it is shown that the bearing capacity for inelastic projects can be increased severalfold as compared to thermoelastic projects, and reinforcement can be substantially saved in the inelastic case under fixed loading. Despite the worsening of strength characteristics of the composition phases, the bearing capacity of the structure remains almost unchanged upon heating in the inelastic case and can even increase in the thermoelastic case.     

Deflections of uniformly stressed reinforced plates with account for their weakened resistance to the transverse shear

The hypotheses of the Reissner theory are used to formulate the problem of uniformly stressed reinforcement (USR) of transversely bent elastic plates by fibers with a constant cross section. The analysis of the corresponding system of governing equations and boundary conditions is performed. The model problem of USR of rectangular elongated plates subjected to cylindrical bending with various types of loading of one of the longitudinal edges and rigid clamping of the other one. It is shown that there could exist two solutions of the USR problem, one of which is regular and the other one singular. The edge effects occurring in the presence of the torque applied to the edge, which significantly affects both the stress–strain state of the binder material and the reinforcement structure, are revealed.     

Nonlinear bendings of unsymmetrically layered anisotropic rectangular plates

An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under verious supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem.     

Uniformly higher order accurate extrapolations to solutions of uniformly convergent discretization methods for singularly perturbed problems

We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the Il'in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.Supported by the National Natural Science Foundation of China.     

Vanishing Viscosity Method for Transonic Flow

A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant . This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound uniformly away from cavitation for the viscous approximate velocity fields. Mathematical entropy pairs are constructed through the Loewner–Morawetz relation via entropy generators governed by a generalized Tricomi equation of mixed elliptic–hyperbolic type, and the corresponding entropy dissipation measures are analyzed so that the viscous approximate solutions satisfy the compensated compactness framework. Then the method of compensated compactness is applied to show that a sequence of solutions to the artificial viscous problem, staying uniformly away from stagnation with uniformly bounded velocity angles, converges to an entropy solution of the inviscid transonic flow problem. Dedicated to Constantine M. Dafermos on the Occasion of His 65th Birthday     

Elastoplastic Bending of Plates Resting on Elastic Subgrade under Rotational Symmetry Conditions*

An analysis of rotationally symmetric plates resting on an elastic subgrade is presented. The plates are made of an elastic, perfectly plastic material that obeys Johansen's yield condition and associated flow rule. The analysis is simplified by assuming that any plate element is either entirely elastic or entirely plastic. This assumption is practically fulfilled for a sandwich plate. Differential equations that describe the behavior of plastic zones during the deformation process are derived and solved in closed form. Examples of solutions for uniformly loaded circular plates are given.     

On the stress distribution in a prestretched simply supported strip containing two neighboring circular holes under forced vibration

The three-dimensional linearized theory of elastic waves in initially stressed bodies under plane strain is used to study the influence of the initial stretching of a simply supported plate strip with two neighboring circular holes on the stress concentration around the holes caused by additional uniformly distributed dynamic (time-harmonic) normal forces acting on the upper face. The corresponding problem is formulated and solved by the finite-element method. Numerical results on the stress concentration around the holes and the influence of the initial stretching on this concentration are presented Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 135–140, October 2007.     

旋转圆盘受均布压力作用时的摄动分析

本文对中心带轴匀速旋转圆盘在均布压力作用下的受力及变形问题进行了摄动分析，得到了受载条件为Ｊ＾２／ＪＨ＜＜１时，圆盘应力及形变的渐近解。其形变渐近解为Ｗｈｉｔａｋｅｒ函数形式比较表明，渐近解与Ｃｈｅｂｙｓｈｅｖ数值解有较好的一致性。     

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar.anisotropic. materials. Integrating Riemann-Schwarz＇s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors, at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.     

SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION

IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1～6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7～11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem…     

Uniformly moving screw dislocation interacting with interface cracks in anisotropic bimaterials

This paper attempts to investigate the problem for the interaction between a uniformly subsonic moving screw dislocation and interface cracks in two dissimilar anisotropic materials. Using Riemann–Schwarz’s symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interface containing one and two cracks. The expressions of stress intensity factors at the crack tips and image force acting on moving dislocation are derived explicitly. The results show that the stress intensity factors at the crack tips decrease with increasing velocity of dislocation, and larger dislocation velocity leads to the equilibrium position of dislocation leaving from crack tips. The presented solutions contain previously known results as the special cases.     

Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws

We consider the problem of self-similar zero-viscosity limits for systems ofN conservation laws. First, we give general conditions so that the resulting boundary-value problem admits solutions. The obtained existence theory covers a large class of systems, in particular the class of symmetric hyperbolic systems. Second, we show that if the system is strictly hyperbolic and the Riemann data are sufficiently close, then the resulting family of solutions is of uniformly bounded variation and oscillation. Third, we construct solutions of the Riemann problem via self-similar zero-viscosity limits and study the structure of the emerging solution and the relation of self-similar zero-viscosity limits and shock profiles. The emerging solution consists ofN wave fans separated by constant states. Each wave fan is associated with one of the characteristic fields and consists of a rarefaction, a shock, or an alternating sequence of shocks and rarefactions so that each shock adjacent to a rarefaction on one side is a contact discontinuity on that side. At shocks, the solutions of the self-similar zero-viscosity problem have the internal structure of a traveling wave.     

Frictionless indentation by an elastic punch: a dynamic Hertzian contact problem

Frictionless indentation of an elastic half-plane by a relatively blunt, symmetric elastic punch at an ar: bitrary speed is analyzed by treating the more general problem of frictionless Hertzian contact between elastic solids. As in the quasi-static problem, the analysis assumes that the solid surface contours are approximately flat. In addition, the contact strip expands at a constant rate and the imposed rigid body motions and surface contours are represented by polynomial curves. Homogeneous function techniques allow analytic solutions to the basic mathematical problem. As an example, the general results are then applied to the uniformly accelerating parabolic punch on a half-plane.     

On aspects of damping for a vertical beam with a tuned mass damper at the top

In this paper, the wind-induced, horizontal vibrations of a vertical Euler–Bernoulli beam will be considered. At the top of the beam, a tuned mass damper (TMD) has been installed. The horizontal vibrations can be described by an initial-boundary value problem. Perturbation methods will be applied to construct approximations of the solutions of the initial-boundary value problem, and it will be shown that the TMD uniformly damps the oscillation modes of the beam. In the analysis, it will be assumed that damping, wind-force, and gravity effects are small but not negligible.     

黏弹性半空间体内部作用水平力时的理论分析

研究假定半无限体为线性黏弹性介质,土体在内部水平集中力作用下的应力球张量和应变球张量之间符合弹性关系,而应力偏张量和应变偏张量之间符合三参数固体黏弹性应力应变关系.利用半空间体内部受水平向集中力的Mindlin弹性理论解,根据弹性--弹黏性相应原理,系统推导了水平集中力作用在半无限体内部时的应力与位移分量的黏弹性解.通过对应力与位移分量在拉氏域内的解答进行Laplace逆变换,给出了应力与位移分量的时域解.作为黏弹性解答的应用,基于上述解答给出了水平向均布荷栽下作用在半空间体内部时的黏弹性位移计算公式,并编制了便于工程应用的计算程序.结果验证与深埋锚板的算例分析表明,本文的理论解答对实际工程具有一定的理论及应用价值.     

Note on the Bending of an Annular Sector Plate Resting on an Elastic Foundation

Abstract

An approximate solution is presented for the bending problem of an annular sector plate resting on a Winkler-type elastic foundation. As a numerical example, the case of a semicircular plate under a uniformly distributed load and having clamped curved edges has been considered.     

The solution of dynamic Point-Ring-Couple in an elastic space and its properties

The solution of dynamic Point-Ring-Couple at the origin,on z=0 plane,in an elastic space is presented and its properties are discussed.Let shocking loads be uniformly distributed,along the direction of circumference,at a circle,on z=0 plane,with radius a and centered at the origin.Then,the solution of our problem is obtained via integral calculation for a→0.When the intensity of this dynamic Point-Ring-Couple is varied with sinωt,the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis,become zero stressed surfaces at any time instance.The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sinωt is found.     

Cross-section optimization of tower crane lattice boom

This paper discusses the problem of cross-section optimization of tower crane lattice boom. The trapezoid cross section has been analyzed. The triangular and rectangular cross sections have also been analyzed as special cases. Total mass of the construction has been selected as the objective function. Optimization parameters have been determined by Lagrange’s multipliers method. Criterion of stress is used as the constraint function. Numerical examples are performed by usage of the obtained theoretical solutions. Those results were than compared with ones obtained by usage of finite element method based computer program. On the base of the analysis that was carried out, the recommendations are given regarding the application of trapezoid, triangular and rectangular cross sections of the lattice constructions.     

Bending of annular sectorial Mindlin Plates using Kirchhoff results

This study is concerned with the elastic bending problem of a class of annular sectorial plates whose radial edges are simply supported. Exact bending relationships between the Mindlin plate results and the corresponding Kirchhoff plate solutions have been derived based on the concept of load equivalence. These bending relationships facilitate the deduction of thick (Mindlin) plate results from the corresponding classical thin (Kirchhoff) plate solutions, thus bypassing the need to solve the more complicated governing equations of thick plates. The correctness of the relationships is established by solving the bending problem of annular sectorial plates under a uniformly distributed load and comparing the results with existing thick plate solutions.     

Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.