Finite element study on minimization of stress concentration factors of finite plate with multi-holes 降低含多孔帶板應(yīng)力集中的有限元研究
Finite element analysis of dynamic stress concentrations for a central circular hole in a finite plate 含中心圓孔有限板動應(yīng)力集中問題的有限元分析
The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite plate, and the analytical solution are obtained 摘要利用裂紋線場方法對巖石材料偏心裂紋板受剪應(yīng)力作用時進行了彈塑性分析,并且獲得了理論解。
Using the complex potential method in the plane theory of elasticity of an anisotropic body, a series solution to the stress field of a finite plate containing multiple cracks subjected to arbitrary loads is obtained by means of the faber series expansion, and the stress intensity factors at the crack tips are calculated based on the theories of fracture mechanics . equivalence yield stress is introduced in order to consider the effects of the plastic zones, with which the strip yield criteria is developed in the article so that the effects of structural size and the crack interactions on the stress distribution can be considered accurately . the effects of plate size, crack size and crack distributions on the stress intensity factors as well as the residual strength of the plate are studied detailedly 采用各向異性體平面彈性理論中的復(fù)勢方法,以faber級數(shù)為工具,得到了含多裂紋有限大板在任意載荷作用下應(yīng)力場的級數(shù)解,并應(yīng)用斷裂力學(xué)方法確定裂紋尖端的應(yīng)力強度因子;引入當(dāng)量屈服應(yīng)力考慮裂尖塑性區(qū)的影響,提出基于帶屈服準則的剩余強度分析模型,能夠充分考慮結(jié)構(gòu)尺寸和裂紋之間相互作用對應(yīng)力場的影響;通過數(shù)值計算詳細討論了結(jié)構(gòu)尺寸和裂紋之間位置關(guān)系對應(yīng)力強度因子和結(jié)構(gòu)剩余強度的影響規(guī)律,得到了一系列對工程應(yīng)用具有實用價值的結(jié)論。
By using the arrived fundamental solution, combined with the " pseudo-traction " method and the boundary collocation, the stress intensity factor for crack in a finite plate under compressive loading are solved, the effects of crack direction and boundary condition on the stress intensity factor are analyzed, and the varying curves of the sif along with the width are given 將所得的基本解與“偽力法”、邊界配置法相結(jié)合,得到了有限板在壓縮荷載作用下應(yīng)力強度因子的解法,分析了裂紋方向和邊界條件對應(yīng)力強度因子的影響,給出了應(yīng)力強度因子隨板寬的變化曲線。
The study indicate that the surface form has no effect on kl, but has obvious effect on kll, and will affect the breaking angle and mode; in finite plate, the boundary condition has effect on the sif and the k is bigger than in infinite plate; the effect of the distance and the angle between cracks are all have obvious effects on the multiple crack interaction, and the interactions between cracks also have obvious effects on the sif, which can be neglect only when the distance is bigger enough 研究表明:裂面狀態(tài)對k_的大小沒有影響,而對k_的影響卻很大,相同應(yīng)力條件下,裂面狀態(tài)會影響裂紋的開裂角和開裂方式;有限板的邊界對應(yīng)力強度因子有一定的影響,其k比無限板中的k略大;裂紋間的距離、夾角等因素對裂紋間的干涉效應(yīng)均有較大影響,裂紋間的干涉效應(yīng)對應(yīng)力強度因子的影響非常顯著,只有當(dāng)裂紋間的距離充分大時,干涉效應(yīng)才可忽略。
The solutions include : the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line, law that the length of the plastic zone along the crack line is varied with an external loads, the maximum lengths of the plastic zone, the bearing capacity of a finite plate with an eccentric crack loaded by shear forces 這個解包括:裂紋線附近彈塑性邊界上的單位法向矢量,裂紋線附近的彈塑性解析解、最大塑性區(qū)長度、裂紋線上的塑性區(qū)長度隨荷載的變化規(guī)律及其承載力。