發(fā)布時(shí)間：2018-08-06 09:05

【摘要】：固體殼單元是一種對(duì)于具有板殼類拓?fù)涮匦缘墓こ探Y(jié)構(gòu)進(jìn)行高效有限元分析的新型三維有限元模型,被廣泛地應(yīng)用于非線性板殼、復(fù)合材料層合結(jié)構(gòu)以及金屬薄板沖壓成型等領(lǐng)域。但是目前固體殼單元的研究還遠(yuǎn)不夠完善,容易出現(xiàn)各種自鎖現(xiàn)象,因此近年來固體殼單元的開發(fā)也成為國(guó)際計(jì)算力學(xué)界的研究熱點(diǎn)。四節(jié)點(diǎn)膜單元是在考慮面內(nèi)彈性變形問題以及四節(jié)點(diǎn)板殼單元的開發(fā)中應(yīng)用最廣泛的一種二維有限元模型。由于最早提出的基于位移法的雙線性Q4單元在承受面內(nèi)彎曲的情況時(shí)容易出現(xiàn)剪切自鎖現(xiàn)象,幾十年來專家學(xué)者們一直致力于精確、高效、可靠的平面四節(jié)點(diǎn)膜單元的開發(fā),這對(duì)平面單元列式的理論基礎(chǔ)創(chuàng)新和更加高效地解決工程問題都具有重要的現(xiàn)實(shí)意義。鑒于上述兩種單元的研究現(xiàn)狀與應(yīng)用前景,本文的研究工作主要包括以下內(nèi)容:本文采用擬協(xié)調(diào)元方法推導(dǎo)了一個(gè)具有顯式單元?jiǎng)偠染仃嚨陌斯?jié)點(diǎn)固體殼單元。該單元每個(gè)節(jié)點(diǎn)僅具有3個(gè)位移自由度,共計(jì)24個(gè)節(jié)點(diǎn)位移參數(shù)。根據(jù)固體殼單元中各應(yīng)力分量的特點(diǎn),擬協(xié)調(diào)固體殼單元在單元內(nèi)假設(shè)了合理的應(yīng)變場(chǎng),從而可有效地避免固體殼單元中容易出現(xiàn)的各種自鎖現(xiàn)象。擬協(xié)調(diào)固體殼單元的另一個(gè)顯著優(yōu)點(diǎn)是可以得到顯式單元?jiǎng)偠染仃?這極大地提高了所得單元的計(jì)算效率。此外,本文還采用了基于彈性力學(xué)平面問題解析解的位移試探函數(shù)近似單元圍面上的位移場(chǎng),從而提高所得固體殼單元的計(jì)算精度。算例表明,本文所給出的八節(jié)點(diǎn)擬協(xié)調(diào)固體殼單元不僅有效地克服了剪切自鎖,而且擁有很高的計(jì)算效率和良好的計(jì)算精度。在笛卡爾直角坐標(biāo)系內(nèi),本文利用擬協(xié)調(diào)元方法構(gòu)造一個(gè)四節(jié)點(diǎn)四邊形平面單元,相應(yīng)的每個(gè)節(jié)點(diǎn)具有兩個(gè)位移自由度(屬于Q4類型膜單元)。該精確、高效的四節(jié)點(diǎn)擬協(xié)調(diào)膜單元的假設(shè)應(yīng)變場(chǎng)僅有五個(gè)獨(dú)立的應(yīng)變參數(shù),并且考慮了泊松效應(yīng)的影響;此單元假設(shè)應(yīng)變場(chǎng)還與由平面彈性問題控制方程給出的位移解析解相一致協(xié)調(diào)。此外,本文還給出在1991年提出的另一個(gè)基于假設(shè)應(yīng)變場(chǎng)的四節(jié)點(diǎn)膜單元的性能考核。以上兩個(gè)四節(jié)點(diǎn)膜單元均沒有任何單元內(nèi)部參數(shù),并且在確定應(yīng)變參數(shù)時(shí)不涉及任何數(shù)值積分,它們的單元?jiǎng)偠染仃嚲稍诘芽栔苯亲鴺?biāo)系內(nèi)顯式地計(jì)算出來。因此,這兩個(gè)四節(jié)點(diǎn)擬協(xié)調(diào)膜單元的列式極其簡(jiǎn)單,具有非常高的計(jì)算效率;同時(shí)它們均能夠通過分片試驗(yàn),無剪切自鎖。與其他四邊形膜單元的數(shù)值結(jié)果對(duì)比表明這兩個(gè)四節(jié)點(diǎn)擬協(xié)調(diào)四邊形膜單元不僅可靠穩(wěn)定,而且給出的位移和應(yīng)力結(jié)果都非常精確。
[Abstract]:Solid shell element is a new kind of three-dimensional finite element model which is widely used in nonlinear plate and shell, which is used for efficient finite element analysis of engineering structures with the topological characteristics of plates and shells. Composite laminated structure and metal sheet stamping and other fields. However, the research of solid shell element is far from perfect, and it is easy to appear various self-locking phenomena. Therefore, in recent years, the development of solid shell element has become a research hotspot in the field of international computational mechanics. Four-node membrane element is the most widely used two-dimensional finite element model in the consideration of in-plane elastic deformation and the development of four-node plate-shell element. Since the first bilinear Q4 element based on displacement method is prone to shear self-locking when it is subjected to in-plane bending, experts and scholars have been devoting themselves to the development of accurate, efficient and reliable planar four-node film element for decades. This is of great practical significance to the theoretical foundation innovation of plane element formulation and to solving engineering problems more efficiently. In view of the research status and application prospect of the two kinds of elements mentioned above, the research work in this paper mainly includes the following contents: in this paper, an eight-node solid shell element with explicit element stiffness matrix is derived by using the quasi-conforming element method. Each node of the unit has only 3 degrees of freedom and a total of 24 node displacement parameters. According to the characteristics of each stress component in the solid shell element, the reasonable strain field is assumed by the quasi-conforming solid shell element in the element, which can effectively avoid all kinds of self-locking phenomena which are easy to occur in the solid shell element. Another significant advantage of the quasi-conforming solid shell element is that the explicit element stiffness matrix can be obtained, which greatly improves the computational efficiency of the resulting element. In addition, the displacement-heuristic function based on the analytical solution of the plane problem of elasticity is used to approximate the displacement field on the circumplane of the element, so as to improve the calculation accuracy of the obtained solid shell element. The numerical examples show that the proposed eight-node quasi-conforming solid shell element not only overcomes the shear self-locking effectively, but also has high calculation efficiency and good calculation accuracy. In the Cartesian Cartesian Cartesian coordinate system, a quadrilateral plane element with four nodes is constructed by using the quasi-conforming element method. Each node has two degrees of displacement (belonging to the Q4 type membrane element). The assumed strain field of the four-node quasi-conforming membrane element has only five independent strain parameters, and the Poisson effect is taken into account. This element assumes that the strain field is also consistent with the analytical solution of displacement derived from the governing equation of the plane elastic problem. In addition, the performance evaluation of another four-node membrane element based on the hypothetical strain field proposed in 1991 is also presented in this paper. Neither of the above two four-node membrane elements has any internal parameters and no numerical integration is involved in the determination of strain parameters. Their element stiffness matrices can be calculated explicitly in Cartesian Cartesian coordinate system. Therefore, the formulation of these two quasi-conforming membrane elements is extremely simple and highly efficient, and both of them can pass the shearing self-locking experiment. Compared with other quadrilateral membrane elements, the numerical results show that the two quadrilateral quasi-conforming quadrilateral membrane elements are not only reliable and stable, but also the results of displacement and stress are very accurate.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TB115

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