用双剪统一屈服准则求矩形板的极限荷载

采用俞茂宏双剪统一屈服准则求出了矩形板的塑性极限荷载的统一解,得出不同参数ｂ值对极限荷载的影响曲线,从而得出一系列从Ｔｒｅｓｃａ的单剪屈服准则解到双剪屈服准则（俞茂宏,１９６１）的矩形板极限荷载。文献中已有的Ｔｒｅｓｃａ解为本文的一个特例。     

金属简支圆板在边缘均布载荷作用下的塑性极限解

采用双剪统一屈服准则首次对金属类材料的简支圆板在边缘均布载荷作用下的塑性极限进行求解，得出相应的统一解形式。已有的Tresca准则、vonMises准则、双剪应力准则的解答是文中解答的特例或逼近。并得到圆板的极限载荷随不同屈服准则以及边缘载荷内半径的变化曲线。     

用双剪统一屈服准则求固支圆板的极限荷载

首次采用俞茂宏统一屈服准则对圆支圆板进行了塑性极限荷载分析,得出了固支圆板在均布荷载作用下的统一解形式,对于不同的材料,本文均能出相应的极限荷载,可以广泛应用于机械工程的相关结构中。     

环形板的塑性极限统一解

采用统一强度理论求出了环形板的塑性极限荷载，内力场及速度场的统一解，得出不同参数b值及材料的拉压比α对极限荷载的影响曲线。所给出的解可以灵活使用于各种性能的材料，可以充分反映材料的SD效应及中间主应力效应。文献中已有的Tresca解、Mises解、双剪应力屈服准则解以及双剪统一屈服准则均为本文的特例。     

具有圆孔的大薄板材料的统一极限解

采用俞茂宏统一强度对具有圆孔的大薄板材料进行了极限分析,得到了统一解形式,以往基于Ｔｒｅｓｃａ、Ｍｉｓｅｓ、双剪屈服准则以及Ｍｏｈｒ－Ｃｏｕｌｏｍｂ强度理论的极限解均为本文统一解的特例。     

基于三剪统一屈服准则受内压弯管塑性极限载荷分析

在变壁厚椭圆截面弯管应力分析的基础上,运用三剪统一屈服准则,对承受内压作用的弯管进行了极限载荷分析,推导出考虑弯管截面壁厚变化和弯管椭圆度的变壁厚椭圆弯管的塑性极限压力统一解析解。弯管的极限载荷随着弯管壁厚和弯管椭圆度的不同而变化。     

无缺陷弯管的塑性极限载荷的统一解

采用双剪统一强度理论,分析等厚度薄壁弯管在内压作用下的塑性极限载荷问题,推导出塑性极限载荷统一表达式。在该表达式中,当其系数取不同的值时,就可得到按Tresca屈服准则、双剪统一屈服准则所得的结果,并能较好逼近Mises屈服准则所得的结果。     

小范围屈服条件下裂尖塑性区统一解

采用俞茂宏双剪统一屈服准则求解了Ⅰ、Ⅱ、Ⅲ型裂纹在小范围屈服条件下的塑性区形状与大小的统一解答。已有Tresca准则、Miss准则的解答均是该解答的特例或线性逼近,该解答可以适合于多种工程材料,具有普遍性和适用性,从得出的解析解和图形分析中可以得出一些新的结论。     

等效节点载荷解析解在结构受力分析中的应用

针对非均布载荷作用结构的受力分析问题,从有限元基本原理出发,选取三角形单元对加载边进行等间距网格离散,推导加载边上端点和中间节点处等效节点载荷的解析解,其包含加载边端点坐标、网格数、外加载荷及外加载荷与加载边的夹角。以单向均布轴压作用下斜板的屈曲分析、非均布载荷作用下悬臂矩形板弯曲的弹性力学解为例,在加载边节点上施加解析解对应等效节点载荷。通过对比其他数值解表明,解析解可精确、简便地求解非均布载荷作用结构的受力问题。     

井筒在孔隙压力和渗流作用下的统一极限分析

采用统一强度理论,考虑井筒周围岩石的孔隙压力和渗流作用,对井筒进行弹塑性分析,求出保持井壁稳定的弹性极限载荷和塑性极限载荷的统一解析式。以往基于Mohr-Coulomb强度理论和双剪强度理论的解均为该解的特例。所得的统一解可以用于适合不同强度理论的各类岩石材料的极限分析。     

Plastic limit analyses of circular plates with respect to unified yield criterion

Plastic limit analysis of a circular plate under uniform transverse loading is presented in terms of an unified yield criterion (UYC). Exact and unified solutions of load-carrying capacities, moment fields and velocity fields for simply supported circular plate, clamped circular plate and annular plate in plastic limit state are derived. Moment fields of the three typical circular plates correspond to different distribution fields on the yield curves. Maximum and minimum plastic limit solutions are deduced for the three types of circular plates by selecting the weighted coefficients with upper and lower bound values in the unified yield criterion. Moment fields and velocity fields with respect to the three special criteria, namely the Tresca criterion, the Mises criterion (close-form solution) and the twin shear stress criterion are illustrated and compared. The paper presents an effective analytical method to compute the exact plastic limit solution for circular plates in terms of a piecewise linear yield criterion.     

Limit angular velocity of rotating disc with unified yield criterion

Plastic limit analysis of a rotating solid or annular disc with variable thickness is presented in terms of a unified yield criterion (UYC). Stress distributions of the discs in plastic limit state corresponding to different yield curves are deduced. Upper and lower bounds of the plastic limit solutions are derived by selecting a weighting coefficient in the unified yield criterion. Stress redistribution is solved when the stress field violates yield criterion locally. Limit angular velocity as well as the stress distributions with respect to three special criteria, namely the Tresca criterion, the Mises criterion (close form solution) and the Yu criterion are illustrated and compared. The influences of yield criterion as well as the thickness on plastic limit solution of a rotating disc are demonstrated and discussed.     

金属材料的平面应力非连续分叉

对已有弹塑性体非连续分叉结果进行了修正 ,使其更为合理。在此基础上 ,基于统一屈服准则 ,得出了金属材料非连续分叉的起始方位角以及相应的硬化模量的统一解析解 ,并且分析了不同程度的中间主应力对结果的影响。进而发现所得的结果与屈服准则的选取有关 ,揭示了在分叉研究中正确选取符合金属材料特性的强度准则的重要性。     

Plastic analysis of perforated plates for orthotropic yield criteria

The concept of an equivalent orthotropic material is used in evaluating the collapse loads for perforated plates. Uniformly loaded circular plates are investigated. Limit pressure solutions are obtained for both the simply supported and rigidly built-in edge conditions. Statically admissible radial and circumferential bending moment fields are found and the associated velocity fields are shown to be kinematically admissible. Numerical results are given in dimensionless form covering arbitrary plate geometries over the entire range of material orthotropy.These solutions are quite useful in the plastic analysis and design of perforated plates used as pressure vessel heads, tube sheets, reactor core support plates and the like. Perforated plates have considerably higher effective yield strengths when subjected to equi-biaxial loading than when subjected to loading of arbitrary biaxiality and orientation with respect to the penetration pattern. Thus, the equivalent orthotropic plastic material concept is ideally suited to the analysis of such plates. The resulting limit load pressures are substantially lower than the values obtained using isotropic Tresca yield criterion based on the yield strength for equi-biaxial loading. The results are substantially higher than the values obtained using the maximum isotropic Tresca yield condition falling entirely within the orthotropic yield surface.     

厚壁圆筒安定问题的统一解析解

采用双剪统一强度准则对理想弹塑性材料的厚壁圆筒进行安定性分析,得出了厚壁圆筒加载应力、残余应力及安定极限压力的统一解析解。所得的解不仅能包含以往基于Tresca准则、Mohr—Coulomb准则和广义双剪准则的结果,而且给出一系列新的结果。这些结果能考虑材料的拉压强度差效应及中间主应力效应,因而适应于多种材料。最后,利用所得的解研究了材料的中间主应力效应和拉压强度差效应对厚壁圆筒安定极限压力的影响。结果表明：当考虑材料的拉压强度差效应及中间主应力效应时,厚壁圆筒安定极限压力将明显提高。     

Plastic collapse analysis of thin-walled pipes based on unified yield criterion

Based on a unified yield criterion (UYC), the plastic collapse analysis of thin-walled pipes is conducted in the framework of finite strain. A unified analytical solution for the burst pressure of end-capped defect-free pipes is derived, which is fit for various kinds of non-SD (strength differential) materials. A series of solutions can be deduced from this unified solution, and those solutions of burst pressure on the basis of Tresca, von Mises, ASSY, and TS criteria are special cases of it. By comparing with existing test result, it is found that the present unified solution is very convenient and effective for the prediction of burst pressure.