金属斜板极限载荷的统一解析解

用统一屈服准则(俞茂宏,1991)对斜板进行塑性极限分析,得到斜板的统一极限载荷解析式。从而得到一系列从单剪屈服准则(特雷斯卡,1864)到三剪屈服准则(米泽斯,1913)再到双剪屈服准则(俞茂宏,1961)的各种斜板的极限载荷,并得到矩形板和菱形板的极限均布载荷p随不同屈服准则的变化曲线,文献中已有的解均为统一解析解的特例。本文得到一系列有规则变化的新的解析解,可以适合于各种拉压强度相同的材料以及从方板、矩形板到不同角度的各种斜形板。它的工程应用可以得到显著的经济效益。     

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。     

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。     

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。     

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。     

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。     

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。     

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。     

纤维增强复合压力容器的弹塑性分析

本文研究了圆柱正交异性纤维增强复合压力容器在内压力作用下,弹、塑性的应力解和位移解（采用了Tsai-Hill屈服准则）。给出了弹性极限压力（屈服压力）、极限载荷和安定载荷的公式。并按目前国际上沿用的弹性失效准则、整体屈服设计准则和爆破失效准则[1][4]与各向同性解进行了比较。计算数据表明,用纤维增强复合材料制作的压力容器,不仅弹性极限压力大大提高（K值越大,相对提高值越大）,而且,材料抗变形的能力当K≥0.79时亦有所增加。     

装载机摇臂座梁断裂的修理

一台装载机发生双摇臂反转六连杆动臂座梁箱形结构开焊、断裂事故,现场检查发现座梁断裂处有轻微变形(见附图)。检查发现座梁两边与动臂板刚性连接,座梁耳板受力最大。经计算,正应力和剪应力均在材料的屈服极限范围内;当座梁在偏载荷作用下,最大弯矩发生在正应力最大的那一点。经过计算,该点的正应力、剪应力均在材料的屈服极限范围内。由此可以推断出动臂各铰点应力没有超过材料的屈服极限,工作装置受到水平载荷作用时的受力情况与受到垂直载荷时的相似。     

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.     

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 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。     

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.     

Rigid-plastic collapse of compression-bent shallow shells

Limit analysis solutions are given for simply supported shallow spherical shells under combined external loading. The effect of transverse shear on collapse loads is examined in the paper. Lower bound and exact load interaction curves at collapse are given for several shell configurations. The shell material is assumed rigid-plastic and yields according to the von Mises criterion. The results indicate that the lower bound approach gives acceptable results when extremely shallow shells are considered. It is also shown that the reduction of collapse loads due to transverse shear is of the same order as found for circular plates.     

Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load

The assessment of classical lamination shell theory and first-order shear deformation theory is presented for simply supported finite circular cylindrical hybrid shell with cross-ply composite laminate as elastic substrate under electromechanical static load. Navier-type solutions are obtained and used in threedimensional equilibrium equations and transverse strain—displacement relation to obtain transverse stress components and improved value of deflection. These solutions are assessed by comparison with the threedimensional solution. The error in the two-dimensional shell theories increases as the shell becomes thicker and it is more for the patch loads in comparison to the uniformly distributed and sinusoidal loads.     

The influence of elastic shear deformation on the transverse shear failure of a fully clamped beam subjected to idealized blast loading

The influence of elastic shear deformation on the transverse shear response of a fully clamped beam is investigated in the present paper. The beam is made from a rigid, perfectly plastic material and subjected to a uniformly distributed pressure pulse loading. The elastic shear deformation is idealized by an elastic, perfectly plastic spring with a constant spring coefficient. Analytical solutions are obtained for the transverse shear response, which are then used to predict the occurrence of a transverse shear failure. The method presented in the paper may be extended to study the blast-induced shear failure of other structural elements when the elastic shear deformation needs to be considered.