含弱界面結(jié)構(gòu)斷裂分析中辛方法
發(fā)布時間：2018-09-09 18:23
【摘要】：基于哈密頓體系,提出了一種分析含弱界面彈性材料斷裂問題的辛方法.通過引入對偶變量,建立基本問題的哈密頓體系.在該體系下,問題的解可被辛本征解的級數(shù)形式所表示.利用辛本征解之間的辛共軛正交關(guān)系,以及裂紋面條件、弱界面條件和結(jié)構(gòu)外邊界條件,可確定辛本征解級數(shù)的待定系數(shù),從而得到問題的解.這樣,可以獲得Ⅰ型和Ⅱ型廣義應(yīng)力強(qiáng)度因子解析表達(dá)式.數(shù)值結(jié)果揭示了各種邊界條件對應(yīng)力強(qiáng)度因子的影響,同時也表明該方法對復(fù)雜的混合邊界條件問題更有效.
[Abstract]:Based on Hamiltonian system, a symplectic method for the analysis of fracture problems of elastic materials with weak interfaces is proposed. By introducing dual variables, the Hamiltonian system of basic problems is established. In this system, the solution of the problem can be expressed by the series form of the symplectic solution. By using the symplectic conjugate orthogonal relation between symplectic eigensolutions, crack surface conditions, weak interface conditions and structural outer boundary conditions, the undetermined coefficients of the series of symplectic eigensolutions can be determined and the solution of the problem can be obtained. In this way, the analytical expressions of generalized stress intensity factors of type I and type II can be obtained. Numerical results reveal the influence of various boundary conditions on the stress intensity factor, and it is also shown that the method is more effective for complex mixed boundary condition problems.
【作者單位】： 大連理工大學(xué)工程力學(xué)系;大連理工大學(xué)工業(yè)裝備結(jié)構(gòu)分析國家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(11372070,11302042) “九七三”國家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃資助項(xiàng)目(2014CB046803) 中央高�；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金資助項(xiàng)目(DUT14LK41,DUT14RC(4)39)
【分類號】：O346.1
本文編號：2233204
[Abstract]:Based on Hamiltonian system, a symplectic method for the analysis of fracture problems of elastic materials with weak interfaces is proposed. By introducing dual variables, the Hamiltonian system of basic problems is established. In this system, the solution of the problem can be expressed by the series form of the symplectic solution. By using the symplectic conjugate orthogonal relation between symplectic eigensolutions, crack surface conditions, weak interface conditions and structural outer boundary conditions, the undetermined coefficients of the series of symplectic eigensolutions can be determined and the solution of the problem can be obtained. In this way, the analytical expressions of generalized stress intensity factors of type I and type II can be obtained. Numerical results reveal the influence of various boundary conditions on the stress intensity factor, and it is also shown that the method is more effective for complex mixed boundary condition problems.
【作者單位】： 大連理工大學(xué)工程力學(xué)系;大連理工大學(xué)工業(yè)裝備結(jié)構(gòu)分析國家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(11372070,11302042) “九七三”國家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃資助項(xiàng)目(2014CB046803) 中央高�；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金資助項(xiàng)目(DUT14LK41,DUT14RC(4)39)
【分類號】：O346.1
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