【摘要】：對二維剪切梁單元進行研究,利用平面旋轉(zhuǎn)場理論推導(dǎo)了精確曲率模型.采用幾何精確梁理論構(gòu)建了剪切梁單元彈性力矩陣.通過絕對節(jié)點坐標方法建立了系統(tǒng)的非線性動力學(xué)方程,提出基于旋轉(zhuǎn)場曲率的二維剪切梁單元,并分別引入經(jīng)典二維剪切梁單元和基于位移場曲率的二維剪切梁單元進行比較研究.首先,靜力學(xué)分析證明了所提模型的正確性;其次,特征頻率分析驗證了模型可與理論解符合,收斂精度高,并且能準確地預(yù)測單元固有頻率對應(yīng)的振型;最后,在非線性動力學(xué)問題上,通過與ANSYS結(jié)果對比分析,證明了該模型可有效處理柔性大變形問題,并且與經(jīng)典二維剪切梁單元相比具有緩解剪切閉鎖的優(yōu)勢.因此,本文提出的基于旋轉(zhuǎn)場曲率的二維剪切梁單元在處理幾何非線性問題中具有較大的應(yīng)用潛力.
[Abstract]:The two-dimensional shear beam element is studied and the exact curvature model is derived by using the plane rotation field theory. The elastic force matrix of shear beam element is constructed by using the geometric accurate beam theory. The nonlinear dynamic equations of the system are established by using the absolute nodal coordinate method. A two-dimensional shear beam element based on the curvature of the rotation field is proposed. The classical two dimensional shear beam element and the two dimensional shear beam element based on displacement field curvature are introduced respectively. Firstly, the model is proved to be correct by statics analysis. Secondly, the characteristic frequency analysis verifies that the model can agree with the theoretical solution, has high convergence accuracy, and can accurately predict the mode shape corresponding to the natural frequency of the unit. Finally, on the nonlinear dynamics problem, by comparing with the ANSYS results, it is proved that the model can effectively deal with the problem of large flexible deformation, and it has the advantage of relieving the shear locking compared with the classical two-dimensional shear beam element. Therefore, the two-dimensional shear beam element proposed in this paper based on the curvature of rotation field has great application potential in dealing with geometric nonlinear problems.
【作者單位】： 西北工業(yè)大學(xué)航天學(xué)院航天飛行動力學(xué)技術(shù)重點實驗室;武漢理工大學(xué)機電工程學(xué)院;
【基金】：國家自然科學(xué)基金重大項目(批準號:61690210,61690211);國家自然科學(xué)基金(批準號:61603304,11472213)資助的課題~~
【分類號】：O316
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本文編號：2348666