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.     

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.     

用GM屈服准则解析薄壁筒和球壳的极限载荷

首次将GM（几何中线）屈服准则应用于内压薄壁圆筒和球壳的塑性极限分析,获得了解析解.薄壁筒和球壳极限载荷均为壁厚、内径及材料屈服极限的函数.屈服极限越高、壁厚越大,内径越小,极限载荷越大.与Mises准则、双剪应力准则（TSS）和Tresca准则相比,GM准则解居于TSS和Tresca解之间且靠近Mises解,恰好对应误差三角形中线.按GM准则计算的极限载荷随厚径比的增加而线性增加.     

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。     

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。     

在复杂应力状态下厚壁圆筒的极限分析

应用双剪统一强度理论,考虑材料的拉压异性和同性,推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷计算公式,并且绘制了其极限载荷线图。在这些计算公式中,当其系数取不同的值时,就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果。应用其极限载荷线图,根据其承受的载荷大小,就能判断厚壁圆筒是否达到了屈服极限状态。绘制了在不同屈服准则下的极限载荷线图,以便对其差异进行比较。     

基于双剪统一屈服准则的混凝土矩形板极限荷载的研究

采用双剪统一强度理论（俞茂宏,1991）求出了矩形板的塑性极限荷载的统一解,得出了不同参数b值对极限荷载的影响曲线,从而得出了一系列从Tresca的单剪屈服准则解到双剪应力屈服准则（俞茂宏,1961）的矩形板极限荷载。文献中己有的Tresca解为本文的一个特例。将其用于混凝土矩形板的极限荷载计算,得出了满意的结果。双剪统一强度理论可以给出更符合于各种不同材料特性的合理解。     

几个强度理论的屈服实验研究

根据多种塑性金属的二向和三向拉伸与压缩组合主应力屈服强度实验数据,对Tresca强度理论、Mises强度理论、Mohr-Coulomb强度准则、Beltrami最大能量理论、极限应变能强度理论等几个强度理论计算的相对误差进行了比较分析。结果表明极限应变能强度理论计算的误差在10%以内,为最小。Tresca强度理论、Mises强度理论和Mohr-Coulomb强度准则计算的误差分别为-36%、-27%、-23%,计算结果比试验结果偏保守。Tresca强度理论和Mises强度理论都不适用于拉伸屈服强度和压缩屈服强度相等的材料,该材料的理论剪切屈服强度为拉伸屈服强度的倍。极限应变能强度理论可用于二向和三向拉伸与压缩组合主应力强度计算,在全拉伸和全压缩主应力状态下与Rankine强度理论一致,具有工程应用前景和价值。     

双层组合厚壁圆筒弹脆塑性极限内压统一解

基于三剪统一强度准则和弹脆塑性软化模型,考虑材料的脆性软化和中间主应力效应,推导了双层组合厚壁圆筒弹脆塑性极限内压统一解,探讨了粘聚力、内摩擦角、半径比、强度理论参数和中间主应力系数的影响特性,克服了以往基于Tresca屈服准则、Mises屈服准则或双剪强度理论的理想弹塑性解的不足。研究结果表明：中间主应力、材料模型和脆性软化对厚壁圆筒的极限内压均有显著影响。该文所得统一解具有广泛的适用性和理论意义,不但可退化为现有公式,而且还能得到系列化的新解答,对组合厚壁圆筒的设计及工程应用有重要参考价值。     

GM屈服准则求解Ⅰ型裂尖塑性区

用几何中线(GM)屈服准则求解了Ⅰ型裂尖塑性区的形状与尺寸,对比了基于Mises和Tresca准则的求解结果。表明在平面应变条件下,GM准则求解的塑性区面积在Tresca和Mises结果之间,Tresca塑性区面积最大,Mises面积最小,GM塑性区与Mises塑性区非常接近,三者的塑性区均成哑铃状。在平面应力下,GM和Mises塑性区二者仍最接近并为豆芽状,Tresca的塑性区最大。无论平面应力还是平面应变,GM准则计算结果与Mises结果均有最佳接近度。     

用Mises屈服条件求内边界固支环板的极限荷载

对于环板的塑性极限分析,通常应用最大弯矩极限条件.本文应用Mises屈服条件分析内边界固支环板在线性荷载与均布荷载共同作用下的极限荷载.考虑到Mises屈服条件的非线性,文中采用加权余量法进行分析.根据环板屈服时弯矩的边界条件和平衡方程,选取合适的试函数,并用加权余量法中的子域法进行求解.针对线性荷载的不同分布形式,给出极限荷载的计算公式与数值结果,画出极限荷载的影响曲线,并与最大弯矩极限条件的数值结果进行了比较,说明本文结果是合理的.     

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.     

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.     

Plastic limit analysis of cylindrically orthotropic circular plates

The plastic limit analysis of cylindrically orthotropic circular plates is developed using a piecewise linear orthotropic yield criterion. The yield criterion is a modification of an isotropic formulation that consists of a series of weighted piecewise linear components. The piecewise linear yield criterion enables an analytical solution for the plastic limit load of cylindrically orthotropic circular plates. Plastic limit analysis for both simply supported and clamped circular plates under uniformly distributed load are carried out. Parametric studies are conducted to investigate the sensitivity of the plastic limit loads to material orthotropy and influences of orthotropic ratio and chosen yield criteria on the plastic limit loads of the circular plates are discussed. It is found that the plastic limit loads of the orthotropic circular plates are affected significantly by the orthotropic ratio. Enhancement of the circumferential yield moment will increase dramatically the plastic limit load of the plates. Moment and velocity fields of the plates in plastic limit state are also derived and discussed. The results obtained from the present study are helpful in understanding the failure mechanism of orthotropic circular plates and is useful for design.