环形均布荷载作用下简支圆板的塑性极限分析

本文采用双剪统一屈服准则首次对受环形均布荷载作用下的简支圆板进行了塑性极限分析,得出了相应的统一解形式。已有的Tresca准则、Mises准则、双剪应力准则的解答是文中解答的特例或逼近,它可以适用于不同性状的拉压同性材料。用本文的解还可以推出多种荷载作用下简支圆板的塑性极限荷载。     

基于双剪统一强度理论的圆板塑性极限分析

通过对轴对称弯曲圆板在塑性极限状态下应力和弯曲内力的分布研究,建立了双剪统一强度理论下用弯矩表示的屈服条件,即广义双剪统一屈服条件。该广义双剪统一屈服条件是一条对称的外凸闭合折线,可应用于由各种拉压强度比及剪压强度比材料构成的圆板和环板的塑性极限分析。对均布荷载作用下的简(固)支圆板进行了塑性极限分析,得出了圆板的塑性极限荷载、塑性极限状态时的内力场和速度场,分析了拉压强度比α以及中间剪应力影响系数b对塑性极限承载力的影响。     

横向和中面荷载联合作用下的圆柱正交异性圆板的大变形分析

本文对横向和中面荷载联合作用下的圆柱正交异性圆板的大变形进行了研究。研究是以Ｖｏｎ－Ｋａｒｍａｎ方程组为基础、用Ｇｄｅｒｋｉｎ技术取Ｃｈｅｂｙｃｈｅｖ多项式为试函数进行的。一些特例与有关文献结果吻合很好。某些结论可供设计圆板时参考。     

均布载荷作用下简支圆板塑性极限载荷的解析解

该文建立了受均布载荷作用简支圆板运动许可应变场,并首次以EA(等面积)屈服准则进行了塑性极限分析,获得了极限载荷的解析解。该解为圆板半径a、圆板厚度h以及屈服强度的函数。与Tresca、TSS以及Mises解比较表明,Tresca屈服准则预测极限载荷的下限,TSS屈服准则预测极限载荷的上限,EA和Mises屈服准则预测的极限载荷恰居二者中间,且EA解几乎与Mises解重合。此外,该文还讨论了挠度与相对位置r/a之间的变化关系。     

比塑性功求解线性载荷下简支圆板极限载荷

为了获得线性载荷作用下的简支圆板极限载荷的解析解,本文提出了刚塑性第一变分原理的运动许可应变场,并首次以GM(几何中线)屈服准则塑性比功进行了塑性极限分析.首次获得了GM准则下圆板极限载荷的解析解,该解为圆板半径a、材料屈服极限σs及板厚h的函数.与Tresca、TSS及Mises预测的极限载荷比较表明:Tresca准则预测极限荷载下限,TSS屈服准则预测极限载荷的上限,GM屈服准则比塑性功解析结果恰居于两者之间;GM解略低于Mises解,两者相对误差为3.38%.此外,文中还讨论了挠度与相对位置r/a之间的变化关系.     

Computations in limit analysis for plastic plates

A class of mixed finite element discretizations of the problem of limit analysis for plastic plates is analysed. For the discrete problem we discuss a linear programming approach based on linearization of the yield condition and a convex programming approach based on the exact Mises condition. Applying the method to rectangular plates with uniform load and concentrated loads we get improved and new results partly in disagreement with one of our references.     

A finite element,linear programming methods for the limit analysis of thin plates

Finite elements having linear moment distributions and use of linearized yield criteria allow one to determine lower bounds to the collapse load of thin plates as solutions of linear programs. The method is quite general and rigorously meets the requirement of the lower bound theorem of limit analysis for concentrated or line load distributions. Ways of treating distributed surface loads are also discussed and tested. Actual bounds are computed for a variety of plate problems governed by Tresca yield criterion and compared with previous solution obtained from higher order stress elements and non-linear optimization techniques. The comparison shows that the present method can yield accurate bounds with considerably shorter computer times and relatively small number of elements. Additional tests show that numerical convergence to the limit loads is assured by suitable refinement of the mesh pattern.     

Effect of plastic anisotropy of weld on limit load of undermatched middle cracked tension specimens

Plastic anisotropy may have a significant effect on the limit load of structures. The present paper shows its effect on the limit load of well‐undermatched middle cracked tension specimens assuming that the base material is elastic and the weld material obeys Hill's quadratic orthotropic yield criterion in rigid‐perfect plasticity. The solution is based on a kinematically admissible velocity field, which is compatible with a stress field satisfying the equilibrium equations and the yield criterion in the plastic zone. The velocity field is singular in the vicinity of the bi‐material interface, which is typical for isotropic materials.     

Effect of plastic anisotropy on the limit load of highly undermatched welded specimens in bending

Plastic anisotropy is a typical property of many metals and it can have a significant effect of the limit load of structures. It is therefore of importance to evaluate this effect for typical geometries covered by compendia of flaw assessment procedures for limit load solutions. The present paper deals with a typical highly undermatched specimen in pure bending. It is assumed that the mismatch factor (the ratio of the yield stress of weld material to the yield stress of base material) is so small that plastic deformation solely occurs in the weld whereas the base material is elastic (rigid). The weld material obeys Hill’s quadratic orthotropic yield criterion. The variation of the upper bound bending moment with the thickness of the weld and anisotropic properties of the material is illustrated. Comparison with the isotropic case made shows that an effect of plastic anisotropy can be quite large.     

Linear buckling analysis of orthotropic inhomogeneous rectangular plates under uniform in-plane compression

Summary A linear buckling analysis is carried out for orthotropic inhomogeneous rectangular plates under uniform in-plane compression. It is assumed that material inhomogeneities of Young's modulus and shear modulus of elasticity are continuously changed in the thickness direction with the power law of the coordinate variable, while Poisson's ratio is assumed to be constant. The buckling equation can be successfully constructed as the linearized von Kármán plate model by introducing the newly defined position of the reference plane which enables us to easily deal with the problem. The critical buckling loads of the simply supported rectangular plate are presented using the derived fundamental relations. Effects of material inhomogeneity, material orthotropy, aspect ratio, width-to-thickness ratio and load ratio are discussed.     

Shear and bending deformation of rigid-plastic circular plates by central pressure pulse

The dynamic plastic deformation of simply supported and clamped circular plates to a central pressure pulse is investigated theoretically. The plate material is assumed to be rigid-perfectly plastic and to obey a yield criterion which retains the transverse shear force as well as bending moments. Various patterns of deformation are obtained for a wide range of parameters which combine plastic bending and shear sliding. The dependence of the final central deflection and shear displacement on the relative shear strength, the load magnitude and the loaded area are discussed for a short duration pressure pulse. The influence of boundary conditions on shear and bending deformation is examined.     

MY准则解析受内压薄圆环极限压力

目的探明受内压薄圆环极限承压能力。方法首次以MY(平均屈服)准则对受内压薄圆环进行弹塑性分析,克服Mises准则数学求解的困难性,导出塑性区内的应力场,并获得塑性极限压力的解析解。此外,还给出了弹塑性临界半径与内压之间的依赖关系,并分析了二者间的变化规律。结果塑性极限压力的解析解表明,塑性极限压力是材料屈服强度、半径比值的函数;与已有的Tresca、TSS准则获得的结果比较表明,Tresca准则给出极限压力下限,TSS屈服准则给出极限压力上限,MY准则给出极限压力居于两者之间,可作为Mises解的替代。结论文中结果对于充分发挥材料性能,进而对薄圆环的设计、选材以及安全评估具有实际工程意义。     

Perforation of rigid-plastic plate by blunt missile

Three rigid plastic models are presented to treat circular plate deformation during perforation by a rigid missile; these models are based on different assumptions for yield. The analysis considers plate bending, stretching and also shear around the periphery of a central plug. An equivalent strain failure criterion is developed that includes the influence of both shear and radial tensile strain on localized failure of the plate. Both this and a pure shear failure criterion of Shadbolt et al. [1] are used together with three structural deformation models to calculate the ballistic limit and final deformed profiles of plates. These calculations are compared with some experimental results for plates of different materials.     

MY准则解析受均布载荷简支斜板极限载荷

为了得到斜板极限载荷的解析解,用平均屈服(MY)准则,对受均布载荷的简支金属斜板进行了塑性极限分析.首次获得MY准则下斜板极限载荷的解析解,该解是斜板几何参数长l1,宽l2以及长宽夹角θ的函数.研究表明:随着θ的增大,极限载荷先增大而后减小;斜板面积增加,极限载荷减小.得到了菱形、矩形和方形板的解析解,并将方形板的解析解与Tresca、Mises以及TSS提供的极限载荷进行比较,对比表明:方板的极限载荷与边长成反比关系,Tresca屈服准则提供极限载荷的下限,TSS屈服准则提供上限,MY准则预测结果恰居二者中间,且最靠近Mises解.     

Influence of anisotropy on the limit load of bi-material welded cracked joints subject to tension

A plane-strain upper bound limit load solution for bi-material welded joints subject tension is found. It is assumed that each material obeys Hill's orthotropic yield criterion and one of the principal axes of orthotropy coincides with the tensile direction. A crack of arbitrary length is located at the bi-material interface. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. The main purpose of the paper is to demonstrate that the influence of anisotropy on the magnitude of limit loads may be much more significant than other effects.     

A duality theorem for plastic plates

Summary Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities are mathematically incomplete. A duality theorem equates the greatest lower bound and the least upper bound. Although some general statement has been made on the duality relation of limit analysis, each yield criterion will lead to a specific duality theorem. The duality theorem for a class of plastic plates is established in this paper. The family of -norms is used to represent the yield functions. Exact solutions for circular plates under a uniform load are obtained for clamped and simply supported boundaries as examples of the specific duality relations. Two classical solutions associated with Tresca and Johansen yield functions are also presented in the spirit of their own duality relations, providing interesting comparison to the new solutions. A class of approximate solutions by a finite element method is presented to show the rapid mesh convergence property of the dual formulation. Complete and general forms of the primal and dual limit analysis problems for the -family plates are stated in terms of the components of the moment and curvature matrices.With 6 Figures     

Nonlinear analysis of smart functionally graded annular sector plates using cylindrically orthotropic piezoelectric fiber reinforced composite

This work deals with the geometrically nonlinear thermo-electro-elastic analysis of functionally graded (FG) annular sector plates integrated with the annular patches of cylindrically orthotropic piezoelectric fiber reinforced composite (PFRC). The annular patches with an external voltage across their thickness act as the distributed actuators and their performance in controlling the nonlinear flexural deformations of the host FG plates is investigated. The temperature field is assumed to be spatially uniform over the plate surfaces and varied through the thickness of the substrate FG plates. The temperature-dependent material properties of the FG plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson’s ratio is assumed to be a constant over the domain of the substrate plate. A finite element model of the overall smart FG annular sector plate is developed based on the first order shear deformation theory and the Von Karman nonlinear strain–displacement relations. The governing nonlinear finite element equations are derived employing the principle of minimum potential energy and solved using direct iteration method. The numerical results illustrate significant control authority of the cylindrically orthotropic PFRC annular patches for active control of nonlinear deformations of the substrate FG annular sector plates. The numerical results also reveal the best radial and circumferential locations of the annular PFRC patches for effective control. For a specified circumferential stretch of the annular PFRC patches, their minimum radial length is numerically estimated in such a way that the performance of the overall smart FG plate is not affected significantly. The effects of the material properties and the temperature of the host FG plate on the performance of the annular PFRC patches are also discussed.     

Dynamic plastic response of a circular plate based on unified strength theory

The study and design of structures under dynamic loads require a knowledge of the plastic response and deformation behavior under impact loading. The calculations of dynamic plastic response of structures are useful for the design and investigation of colliding vehicle, engine and various impacting structures. The unified solutions of dynamic plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are introduced. The strength is different in tension and compression and the effect on the yield criteria is taken into account by using the unified strength theory. Upper bound and lower bound plastic responses of the plate, under moderate partial uniformly distributed impulsive loading, are obtained. The static and kinematical admissibility of the dynamic plastic solutions are discussed. The unified solutions of the static plastic load-carrying capacities, moment fields and velocity fields of a simply supported circular plate are also obtained according to the dynamic solutions in this paper. The solutions are suitable for many materials with or without different strengths in tension and compression and the effect of intermediate principal stress.The solutions based on the Tresca, the von Mises, the Mohr–Coulomb theory, and the twin-shear strength theory, as well as the unified yield criterion, are all the special cases of the unified solutions. The influences of the coefficient of failure criteria, b, and tension-compression strength ratio, α, on the dynamic and static solutions, are investigated. It is shown that the effects of different strengths in tension and compression and yield criteria on the dynamic load-carrying capacity are greater than in the static plastic limit state.     

圆形筒仓的塑性极限载荷

本文研究了圆形筒仓的圆柱壳仓壁的塑性极限载荷。筒仓仓壁受到的水平压力和竖直摩擦力按Ｊａｎｓｓｅｎ公式分布。文中分析了３种塑性破坏机构，并给出了无量纲极限载荷随结构参数的变化曲线。     

Influence of anisotropy on a limit load of weld strength overmatched middle cracked tension specimens

ABSTRACT A plane‐strain upper bound limit load solution for weld strength overmatched middle cracked tension specimens (M(T) specimens), is found. It is assumed that the weld material is isotropic, but the base material is orthotropic and its axes of orthotropy are straight and parallel to the axes of symmetry of the specimen. A quadratic orthotropic yield criterion is adopted. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. These two solutions are compared to demonstrate the influence of anisotropy on the magnitude of the limit load.