开孔薄板的变分原理及屈曲和过屈曲分析的有限元方法

本文以开孔薄板大挠度问题的一般理论为基础,建立了以挠度 w 和应力函数F为未知量的变分原理,并由此建立了用于分析开孔薄板屈曲和过屈曲问题的有限单元法可以看到由于区域的多连通性,单元性质是较为复杂的。     

Variational principles of perforated thin plates and finite element method for buckling and post-buckling analysis

On the basis of the general theory of perforated thin plates under large deflections^{[1, 2]}, variational principles with deflectionw and stress functionF as variables are stated in detail. Based on these principles, finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated, owing to the multiple connexity of the region. Project supported by National Natural Science Foundation of China.     

载电流简支杆的磁弹性屈曲和过屈曲

讨论了磁场中载电流简支杆的非线性稳定性问题，其磁场由两根无限长平行直导线产生，并且自然状态的简支杆位于两导线的中间．结果表明，两导线间的距离和电流方向对杆过屈曲的性态有着显著的影响．     

Resonant-triad instability of a pre-stressed incompressible elastic plate

The dynamic stability properties of a pre-stressed incompressible elastic plate are studied in this paper with respect to perturbations in the form of one near-neutral mode and two non-neutral modes interacting resonantly. The pre-stresses are assumed to be an all-round pressure. With the aid of a novel derivation procedure, the evolution equations governing the scaled amplitudes of the three modes are found to be given by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaCa% aaleqabaGaaGOmaaaakiaadgeadaWgaaWcbaGaaGymaaqabaGccaGG% VaGaamizamaaBaaaleaacqaHepaDdaahaaadbeqaaiaaikdaaaaale% qaaOGaeyypa0JaeyOeI0Iaam4yamaaBaaaleaacaaIWaaabeaakiaa% dgeadaWgaaWcbaGaaGymaaqabaGccqGHsislcaWGJbWaaSbaaSqaai% aaigdaaeqaaOGaaiiFaiaadgeadaWgaaWcbaGaaGymaaqabaGccaGG% 8bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamyAaiabeo7aNnaaBa% aaleaacaaIXaaabeaakiqadgeagaqeamaaBaaaleaacaaIYaaabeaa% kiqadgeagaqeamaaBaaaleaacaaIZaaabeaaaaa!5308!\[d^2 A_1 /d_{\tau ^2 } = - c_0 A_1 - c_1 |A_1 |^2 - i\gamma _1 \bar A_2 \bar A_3 \], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadg% eadaWgaaWcbaGaaGOmaaqabaGccaGGVaGaamizaiabes8a0jabg2da% 9iabeo7aNnaaBaaaleaacaaIYaaabeaakiqadgeagaqeamaaBaaale% aacaaIXaaabeaakiqadgeagaqeamaaBaaaleaacaaIZaaabeaaaaa!4324!\[dA_2 /d\tau = \gamma _2 \bar A_1 \bar A_3 \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadg% eadaWgaaWcbaGaaG4maaqabaGccaGGVaGaamizaiabes8a0jabg2da% 9iabeo7aNnaaBaaaleaacaaIZaaabeaakiqadgeagaqeamaaBaaale% aacaaIXaaabeaakiqadgeagaqeamaaBaaaleaacaaIYaaabeaaaaa!4325!\[dA_3 /d\tau = \gamma _3 \bar A_1 \bar A_2 \], where a bar denotes complex conjugation, is a slow time variable and c ₀, c ₁, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaaigdaaeqaaaaa!387B!\[\gamma _1 \], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaaikdaaeqaaaaa!387C!\[\gamma _2 \], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaaiodaaeqaaaaa!387D!\[\gamma _3 \] are real constants. These equations are solved exactly for the special case when A ₂ and A ₃ have constant amplitudes but time-dependent phases. A series of new post-buckling states, which does not exist when the perturbation is monochromatic, are found. We show that two nonneutral modes can interact resonantly to produce a much larger near-neutral mode, and in particular, two O() non-neutral modes may induce a much larger % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4taiaacI% cacqaH1oqzdaahaaWcbeqaamaalyaabaGaaGOmaaqaaiaaiodaaaaa% aOGaaiykaaaa!3B87!\[O(\varepsilon ^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} )\] oscillation or static post-buckling state. In this sense, resonant-triad interaction is a powerful mechanism in producing high levels of strain and stress in a pre-stressed elastic plate.     

The effect of large rotation on post-buckling of annular plates

On the basis of the axisymmetrical finite deformation theory on Rissner's plates, the post-buckling behaviour of annular plates and the effect of large rotation are qualitatively and numerically discussed by the method of the bifurcation theory.The project is supported by the National Natural Science Foundation of China     

Buckling and post-buckling of piezoelectric plates using finite element method

The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-buckling characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field. The present work is supported by the National Natural Science Foundation of China (No. 59635140).     

弹塑性理想H截面压杆的分支和后屈曲分析

利用一个具有理想H截面杆的弹塑性分析模型,本文阐述了约束直杆自任意低于Karman载荷的初始状态下准静态释放后的全部屈曲过程。其重点在于探讨由杆凸侧逐点变化的弹塑性加卸载历史所产生的影响。     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

含多个分层复合材料层合板后屈曲性态研究

基于Mindlin假定下的大变形板／壳理论，采用参考面单元和虚拟杆单元相结合的非线性有限元方法，建立了分析含多个穿透分层损伤层合板后屈曲行为的有限元计算模型，并给出了考虑接触后非线性屈曲方程的迭代算法，从而研究考虑层间接触效应的多分层层合板的后屈曲性态。文中着重讨论了分层的深度、数目和尺寸对含多分层合板后屈曲性态的影响。大量数值分析结果证明了该模型的有效性，并且得到了一些对层合板结构设计和对含分层损伤层合板评估有益的结论。