本文選題：開孔板結(jié)構(gòu) + 平面應(yīng)力��； 參考：《華中科技大學(xué)》2014年博士論文

【摘要】：含有開孔的各種板結(jié)構(gòu)廣泛地應(yīng)用于工程結(jié)構(gòu)中。由于開孔的存在,其應(yīng)力集中問題和穩(wěn)定性問題是結(jié)構(gòu)設(shè)計(jì)中需要關(guān)注的兩個(gè)重要問題。因此,對(duì)開孔板結(jié)構(gòu)的應(yīng)力及穩(wěn)定性問題進(jìn)行研究具有重要的理論意義和實(shí)用價(jià)值。 本文提出了一種新的求解含有任意開孔形狀有限平板的平面應(yīng)力分布問題和彎曲應(yīng)力分布問題的半解析方法；并在此基礎(chǔ)上,提出了一種新的求解開孔平板和開孔加筋板穩(wěn)定性問題的半解析方法。論文主要的研究工作包括以下幾個(gè)方面： 首先,對(duì)含任意開孔形狀的開孔有限平板在面內(nèi)均布載荷作用下的應(yīng)力分布問題,提出了一種基于平面問題復(fù)變函數(shù)方法的半解析方法,即平面應(yīng)力問題的應(yīng)力函數(shù)重構(gòu)法。這個(gè)方法第一步是考慮含開孔無限大板的情況,通過保角映射變換將在物理平面內(nèi)(z平面)的開孔及開孔外部的無限大區(qū)域映射到映射平面內(nèi)(ζ平面)的單位圓及單位圓外部的無限大區(qū)域。通過Cauchy積分求解得到開孔無限大板在ζ平面內(nèi)的應(yīng)力函數(shù)；第二步是再考慮開孔有限板的情況,在ζ平面內(nèi),將求得的開孔無限大板應(yīng)力函數(shù)的兩組特征項(xiàng)進(jìn)行擴(kuò)展,重新構(gòu)造得到開孔有限板在ζ平面內(nèi)的應(yīng)力函數(shù)；第三步通過最小二乘邊界配置法來確定應(yīng)力函數(shù)未知的待定系數(shù),最終求得開孔有限板的整個(gè)應(yīng)力場(chǎng)。 其次,對(duì)該方法進(jìn)行驗(yàn)證及參數(shù)分析。針對(duì)七種不同開孔形狀的無限大板和有限板,采用該方法進(jìn)行平面應(yīng)力分布計(jì)算,并與有限元ANSYS計(jì)算結(jié)果和已有解析結(jié)果進(jìn)行對(duì)比驗(yàn)證。結(jié)果表明,開孔足夠大時(shí),平面應(yīng)力問題的無限大板理論將不適用,而本文所提出的應(yīng)力函數(shù)重構(gòu)法計(jì)算簡(jiǎn)便、適用性強(qiáng)、計(jì)算精度高,可適用于具有不同開孔形狀的無限板和有限板。采用該方法研究了幾種不同開孔形狀的無限板和有限板分別在單向拉伸、雙向拉伸、剪切載荷作用下,開孔大小對(duì)孔邊應(yīng)力分布和應(yīng)力集中的影響。并針對(duì)矩形開孔的應(yīng)力分布及應(yīng)力集中,進(jìn)一步分析了開孔大小、開孔角度、矩形板邊長(zhǎng)比的影響。 接著,針對(duì)開孔板彎曲應(yīng)力分布問題,基于薄板小撓度彎曲理論的復(fù)變函數(shù)方法,提出了一種新的求解含有任意開孔形狀有限板彎曲應(yīng)力分布問題的半解析方法,即彎曲應(yīng)力問題的應(yīng)力函數(shù)重構(gòu)法。針對(duì)4種不同開孔形狀的無限板和有限板,采用該方法進(jìn)行彎曲應(yīng)力分布計(jì)算,并與有限元ANSYS計(jì)算結(jié)果和已有解析結(jié)果進(jìn)行對(duì)比。計(jì)算結(jié)果表明,該方法適用性強(qiáng)、計(jì)算簡(jiǎn)便、計(jì)算精度高,可適用于具有不同開孔形狀的無限大板和有限板。針對(duì)一對(duì)邊具有均布彎矩作用的4種開孔形狀的無限大板和有限板,采用該方法研究了開孔大小對(duì)孔邊應(yīng)力分布和應(yīng)力集中的影響。 然后,針對(duì)含有矩形開孔的受壓矩形平板總體穩(wěn)定性進(jìn)行了半解析分析。先采用前面提出的求解開孔板平面應(yīng)力分布問題的應(yīng)力函數(shù)重構(gòu)法精確地求解開孔板的內(nèi)力分布。再采用區(qū)域分解法求出含矩形開孔的矩形平板撓曲面函數(shù),該撓曲面函數(shù)不僅滿足開孔板的外邊界條件,還滿足開孔板的內(nèi)邊界條件(矩形孔邊的邊界條件)；基于求得的內(nèi)力分布和撓曲面函數(shù),通過能量法求出其臨界屈曲載荷,并與有限元ANSYS計(jì)算結(jié)果進(jìn)行對(duì)比。計(jì)算結(jié)果表明,該方法計(jì)算精度高。采用該方法討論了在四邊簡(jiǎn)支、四邊固支、承載邊簡(jiǎn)支無載邊自由、承載邊固支無載邊自由四種典型邊界條件下,開孔大小對(duì)其穩(wěn)定性的影響。 最后,針對(duì)含有矩形開孔的受壓加筋板總體穩(wěn)定性進(jìn)行了半解析分析。將加筋板結(jié)構(gòu)簡(jiǎn)化處理為板和梁的組合。與求解開孔平板穩(wěn)定性問題相似,將采用應(yīng)力函數(shù)重構(gòu)法求得的開孔平板的內(nèi)力分布作為開孔加筋板鋪板的內(nèi)力分布；采用區(qū)域分解法求得滿足含矩形開孔加筋板的內(nèi)外邊界條件的撓曲函數(shù)；并進(jìn)一步求得板和梁的彎曲應(yīng)變能及外力功。再通過能量法求出其臨界屈曲載荷,并與有限元ANSYS結(jié)果進(jìn)行對(duì)比。計(jì)算結(jié)果表明,針對(duì)幾種典型開孔加筋板形式,當(dāng)開孔大小在不超過某個(gè)值的范圍內(nèi),計(jì)算結(jié)果誤差較小。在不同邊界條件下,討論了開孔大小對(duì)其穩(wěn)定性的影響。 本文的研究成果對(duì)開孔板結(jié)構(gòu)的理論研究和工程設(shè)計(jì)具有一定的參考價(jià)值。
[Abstract]:The problems of stress concentration and stability are two important issues that need to be paid attention to in structural design due to the existence of openings . Therefore , it has important theoretical significance and practical value to study the stress and stability of open - plate structures .

In this paper , a new semi - analytic method for solving the problem of plane stress distribution and bending stress distribution is presented .
Based on this , a new semi - analytical method for solving the stability problem of open - hole plate and open - hole stiffened plate is presented . The main research work includes the following aspects :

First , a semi - analytic method based on the plane problem recurrence function method is presented , which is the stress function reconstruction method of plane stress problem . The first step of this method is to consider the stress function reconstruction method of plane stress problem . The first step of this method is to take into account the condition of infinite plate with open hole . The first step of this method is to take into account the infinite area outside the unit circle and the unit circle in the mapping plane through conformal mapping transformation . The stress function of the open pore infinite plate in the zeta plane is obtained by Cauchy integral solution .
the second step is to expand the two groups of characteristic items of the open - hole infinite plate stress function , and reconstruct the stress function of the open - hole finite plate in the zeta plane ;
and the third step determines the undetermined coefficient unknown to the stress function by the least square boundary collocation method , and finally obtains the whole stress field of the open - hole finite plate .

In this paper , the method is used to calculate the stress distribution and stress concentration of seven kinds of infinite plates and limited plates with different opening shapes . The results show that the stress distribution and stress concentration of the rectangular openings can be applied to the stress distribution and stress concentration of the rectangular openings , and the influence of the opening size , the opening angle and the ratio of the edge length of the rectangular plate is further analyzed .

This paper presents a new semi - analytical method for solving the problem of bending stress distribution of open - hole plate , which is based on the theory of bending stress of thin plate . A new method for solving bending stress distribution with arbitrary open - hole shape is presented . The results show that the method has strong applicability , simple calculation and high calculation precision . It can be applied to the infinite plate and limited plate with different open - hole shapes .

In this paper , a semi - analytical analysis of the overall stability of a rectangular flat plate with rectangular openings is carried out firstly . The internal force distribution of the perforated plate is solved by the method of stress function reconstruction , which is based on the problem of plane stress distribution of the perforated plate .
Based on the obtained internal force distribution and deflection surface function , the critical buckling load is calculated by the energy method , and compared with the calculation result of finite element ANSYS . The results show that the method has high calculation precision .

Finally , a semi - analytical analysis of the overall stability of the stiffened plate with rectangular openings is carried out . The stiffened plate structure is simplified into a combination of plates and beams . The internal force distribution of the open - hole plate obtained by the stress function reconstruction method is used as the internal force distribution of the open - hole stiffened plate .
The deflection function of the inner and outer boundary conditions of the stiffened plate with rectangular openings is obtained by using the regional decomposition method .
The bending strain energy and external force work of the plate and beam are obtained . The critical buckling load is calculated by the energy method and compared with the result of finite element ANSYS . The results show that the error is less when the opening size is within the range of no more than a certain value , and the influence of the opening size on its stability is discussed under different boundary conditions .

The research results of this paper have some reference value to the theoretical research and engineering design of open - hole plate structure .
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU311

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