具有焊接残余应力的矩形薄板固有频率计算方法研究

利用Galerkin原理,获得了具有对接焊接残余应力矩形簿板各阶振型函数所对应的自由振动方程;得到了具有对接焊接残余应力矩形簿板的固有频率计算方法。研究得出:残余应力越大,固有频率变化越大;频率阶数越高,受残余应力影响越大;材料密度和尺寸a、b越大,固有频率受残余应力影响越小等结论。     

变刚度Winkler地基上受压非均质矩形板的自由振动与屈曲特性

基于经典薄板理论,利用Hamilton原理建立变刚度Winkler地基上受压非均质矩形板自由振动与屈曲问题的控制微分方程并进行无量纲化。通过一种半解析方法-微分变换法(DTM)研究其无量纲固有频率和屈曲临界载荷特性。采用DTM将其无量纲控制微分方程及边界条件变换为等价的代数方程,得到含有频率和屈曲载荷的特征方程。将该问题退化为面内变刚度矩形板情形,其DTM解与精确解进行对比,结果表明DTM具有非常高的精度和很强的适用性。计算出在不同边界条件下屈曲临界载荷并分析地基刚度变化参数、弹性模量变化参数、密度变化参数、面内载荷和长宽比对矩形板无量纲固有频率的影响,给出了不同边界条件下变刚度Winkler地基上受压非均质矩形板的前三阶振型。     

双向受压船体板极限承载能力简易分析方法

采用简易高效的方法分析双向受压船体板极限承载能力,探讨焊接残余变形、残余应力的影响,并根据试验测试结果给出了焊接残余变形容限。计算结果与弹塑性非线性有限元法和试验值进行了比较。最后讨论了腐蚀对船体板极限承载能力的影响。     

筋上有开口裂缝的加筋矩形板横向振动特性分析

利用能量法分析筋上含有开口裂缝的四边简支加筋矩形板的横向振动。将矩形板与加强筋沿交界面切开,再将加强筋沿裂缝分成多个子块,采用薄板弯曲和平面应力理论分别建立矩形板和各子块的横向振动能量方程,解决了传统分析方法需给定开裂处筋的弯曲刚度问题。采用第一类切比雪夫多项式构造矩形板和各子块的位移试函数,由Ritz法和板-筋界面变形连续条件得出含有开口裂缝的加筋矩形板的横向振动特征方程。计算结果与有限元分析结果吻合很好,详细分析了裂缝深度和裂缝位置对无量纲频率的影响。     

460MPa高强钢箱形截面轴压柱局部稳定有限元分析和设计方法研究

为研究460MPa高强度钢材等边箱形截面轴心受压柱的局部稳定受力性能和设计方法, 该文采用有限元软件ANSYS建立有限元模型, 考虑残余应力和局部初始几何缺陷的影响, 对3组共10个460MPa等边箱形截面轴心受压短柱的局部屈曲进行了有限元分析, 并将极限承载力计算值与试验实测值进行对比, 结果证明该模型能够准确分析计算460MPa高强度钢材等边箱形截面轴心受压柱的局部屈曲受力性能。利用该模型进行有限元参数分析, 与钢板的宽厚比相比, 钢板厚度、钢板长宽比、残余压应力值和局部初始几何缺陷幅值等因素对局部屈曲受力性能的影响都很小。将试验实测值和参数分析的结果与中国、美国和欧洲钢结构设计规范中箱形截面局部稳定设计曲线进行对比, 表明现行规范的设计方法不够安全。该文提出的建议设计公式适用于460MPa高强度钢材等边箱形截面轴心受压柱局部屈曲极限应力的设计计算。     

非加劲板抗剪极限承载力

重点研究了板的初始几何缺陷、残余应力、高厚比及边长比等影响因素与抗剪极限承载力的关系,推导出铰接刚性边界焊接板抗剪承载力计算公式。研究表明,初始几何缺陷分布模态、大小和残余应力对板的抗剪极限承载力的影响程度可以忽略不计,从而大大地简化了抗剪板承载力的计算;在经过大量塑性塑动后,较小高厚比受剪板的屈曲后强度有一定的提高,而薄板基本保持不变。     

基于最小能量原理的矩形平面预应力索网结构大变形自由振动研究

以中关村文化商厦30m×70m平面索网为工程背景,考虑矩形索网结构大变形产生的几何非线性的影响,用最小势能原理推导了非线性振动的微分方程并给出了解法;研究了线性振动频率、大振幅振动频率和大变形后小振幅的振动频率计算方法;结合实例对3个振动频率进行了计算分析。给出的非线性振动方程和解法简单准确,为大跨度平面索网结构抗风抗震设计提供参考。     

四角点固定支承矩形板固有特性研究

四角点固定支承矩形板横向振动固有特性的研究对其实际应用及故障诊断具有重要意义。基于能量守恒原理并结合固定支承点处的约束条件建立四角点固定支承矩形板横向振动的拉格朗日方程。采用幂级数多项式来描述其振型函数,根据Rayleigh-Ritz理论推导出四角点固定支承矩形板的横向振动频率方程;由频率方程给出了不同长/宽比矩形板基频的理论计算结果,并应用该方法获得了四角点简支矩形板的频率方程。对典型算例的理论计算结果和有限元分析结果进行比较和分析,给出便于工程应用求解其基频的近似计算式;通过试验研究表明理论计算结果与有限元分析结果和试验结果具有较好的一致性。     

U肋加劲板焊接残余应力的一种简化计算方法

基于焊接残余应力数值模拟方法, 分析了U 肋加劲板各组成板件的板宽、板厚对焊接残余应力分布的影响, 揭示了U 肋与母板残余应力合力的分配规律, 提出了针对不同构造尺寸的U 肋加劲板焊接残余应力分布简化计算方法。研究结果表明:各组成板件的板宽变化对焊接残余拉应力的分布影响较小, 但对焊接残余压应力的大小影响较大;U 肋与母板的板厚比对U 肋与母板残余应力的分配比例影响较大。U 肋加劲板受压承载力计算时, 焊接残余应力分布可以采用简化方法计算, 其结果与根据数值模拟得到的焊接残余应力分布计算的结果基本一致。     

基于简支弹性矩形板含集中质量振动基波频率共形映射解析

借助共形映射理论,采用矩形板边界域奇偶插值点两序列的三角插值方法,寻求了带圆角矩形板等复杂域与单位圆域的共形映射函数;针对含有集中质量振动简支弹性异型板基波频率值的求解,在平面常应力状态下,完成该复杂弹性板以单位圆域方法描述的振动方程,求解板基波频率系数。以带圆角矩形简支板域求解为示例,分析了集中质量大小与位置、矩形长宽比值e、平面常应力系数Sp对基波频率的影响。     

轴向力作用下非对称支承Euler-Bernoulli梁在过屈曲前后的横向自由振动

基于轴线可伸长杆的几何非线性理论，建立了Euler-Bemoulli梁在轴向载荷作用下过屈曲横向自由振动的精确模型，并采用打靶法数值求解了一端可移简支一端固定的Euler-Bemoulli梁在过屈曲前后的小振幅自由振动，获得了线性振动的响应。结果表明，轴向力对过屈曲前后梁的各阶固有频率均有影响。     

Nonlinear analysis of bimodular composite plates under compression

The present work deals with the buckling and post-buckling behaviour of bimodular laminated composite plates. The fiber-governed bimodular constitutive model is adopted for the analysis and the geometrical nonlinearities are accounted for by using the consistent small strain and moderate rotation theory for a shear deformable Mindlin plate. Governing equations of the problem are developed and the finite element formulation is given using lagrangian C°-elements. Some numerical examples are developed to analyze the buckling and post-buckling behaviour of laminated bimodular plates.     

Post-buckling analysis of imperfect laminated plates under combined axial and thermal loads

A post-buckling analysis of composite laminated plates subjected to combined axial compression and uniform temperature loading is presented. The two cases of thermal post-buckling of initially compressed plates and of compression post-buckling of initially heated plates are considered. The initial geometrical imperfection of the plates is taken into account. The analysis uses a perturbation technique to determine buckling loads and post-buckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates. Typical results are presented in dimensionless graphical form.     

The effect of anisotropy on post-buckling behavior of laminated plates using semi-energy finite strip method

The effects of anisotropy (i.e. the ratio of longitudinal modulus of elasticity to transverse modulus of elasticity of a rectangular plate) on buckling and post-buckling performance of laminated plates under uniform end-shortening have been studied in this paper by implementing a Rayleigh–Ritz approach and a finite strip approach based on the concept of a rigorous post-buckling solution for composite plates and plate structures, namely the semi-energy approach. To validate the results, they are compared with those obtained from finite element method of analysis. The study of results has revealed that the buckling and post-buckling response of the laminates is significantly influenced by the changing of the anisotropy ratio.     

An investigation on the post-buckling behavior of symmetric cross-ply laminated plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-buckling analysis of geometrically perfect thin symmetric cross-ply laminated plates under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat laminates. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose ANSYS package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-buckling problem of symmetric cross-ply laminated plates.     

弹性支持任意铺层加筋板的非线性稳定性分析

本文利用能量变分原理和广义傅里叶级数法对具有弹性支持的复合材料任意铺层加筋板在面内各种组合载荷作用下的非线性稳定性特性进行了研究.通过采用牛顿一梯度法数值求解,证明前屈曲压-弯耦合效应对弹性支持的复合材料加筋板的屈曲和后屈曲特性均产生了明显的影响,以致于在压、剪载荷作用的开始即产生了横向翘曲变形.只有当加筋板的四边为夹支时,这种前屈曲耦合效应才不明显.除此之外,还得到了一些与非加筋的层合板完全不同的屈曲和后屈曲特性.所得结果与文献上的相关计算或实验结果对比后均吻合很好,证明本文的理论分析和数值计算是正确有效的.     

Vibration analysis of laminated composite plates with damage using the perturbation method

The present work focuses on vibration characteristics of damaged laminated composite plates. Damage is considered as a local reduction of anisotropic plate stiffness, and three damage factors (representing the damage severity, damage anisotropy, and damage location/area, respectively) are defined to describe damage status in the laminated composite plates. The analytical solutions are obtained by the perturbation method. A numerical analysis is conducted on the vibration of damaged laminated composited plates, and the effect of damage factors on the vibration characteristics is discussed. Results indicate that three damage factors have different influences on the vibration characteristics. Also, the modal curvatures and strain energy show higher damage sensitivity than the natural frequencies and displacement mode shapes. The perturbation-based vibration analysis developed in this study can be used to effectively evaluate the effect of damage on the vibration behavior of anisotropic plates and potentially identify the damage in the laminated plates.     

The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates

The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane–flexural coupling is reported in this paper. The degree of membrane–flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates.

Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation.

Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane–flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness.     

Large deflections of laminated composite plates

A semi-energy approach is formulated for a stability study on laminated composite plates with simply supported edges subjected to uniaxial compression. The analytical approach incorporates the solution of von Karman's fundamental equation for large deflections of plates and consideration of the energy in the buckled-plate system. The effect of coupling responses on the initial buckling load and the immediate post-buckling region is discussed. The results for the initial buckling load are compared with results obtained by the well-known exact solution of Jones. The results for post-buckling behaviour are compared with the experimental data of Rahman.     

考虑剪切效应的轴对称脱层圆板的后屈曲分析

基于Von Karman板理论,考虑横向剪切变形,建立了具脱层的轴对称层合圆板的后屈曲控制方程。应用正交配点法,将后屈曲控制方程、边界条件、以及连续条件转化为非线性方程组,然后进行迭代求解。讨论了不同脱层深度和脱层半径对层合圆板的屈曲及后屈曲特性影响,且与有关文献的结果进行了比较。