复合材料梁的几何精确非线性建模及非经典效应

基于Hodges的广义Timoshenko梁理论对具有任意剖面形状、任意材料分布及大变形的复合材料梁进行几何精确非线性建模,采用旋转张量分解法计算梁内任意一点的应变,采用变分渐近法确定梁剖面的任意翘曲,采用平衡方程由二次渐近精确的应变能导出广义Timoshenko应变能,采用广义Hamilton原理建立梁的几何精确非线性运动方程。将所建模型用于复合材料梁的静动力分析,通过与实验数据的对比,验证了建模方法的准确性,并进一步研究了剖面翘曲及横向剪切变形非经典效应对复合材料梁的影响。研究表明,剖面翘曲对复合材料梁的静变形和固有频率有显著影响,横向剪切变形对复合材料梁的静变形和固有频率的影响与梁的长度/剖面高度比有关。     

A new approach to the finite element modelling of beams with warping effect

As a first step toward developing a finite element formulation that can model coupling among extensional, bending and torsional behaviour of beams, a new method is proposed to properly represent the warping of arbitrary cross-sections. The basic approach is to introduce a small warping displacement superimposed over flat cross-sections of a shear-flexible beam in a deformed configuration. Numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach. The present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation.     

Theory of thin-walled composite beams with single and double-cell sections

In the present work, a mixed beam approach that combines both the stiffness and the flexibility formulation in a unified manner has been performed to analyze the elastically-coupled composite beams with closed cross-sections. The analysis model includes the effects of elastic couplings, shell wall thickness, torsion warping, and constrained warping. The Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. The theory is validated against detailed finite element analysis results for coupled composite beams with single and double-celled box sections. Various layup cases of box beams with bending–torsion or extension–torsion couplings are considered to evaluate whether all the significant non-classical structural effects of composites are captured in the beam theory. Good correlation of the present theory with the finite element analysis is obtained over the different cases. Numerical results showing the accuracy of the approach are demonstrated in the framework of the analysis.     

大变形薄壁复合材料旋转梁静动态特性分析

该文研究了大变形薄壁复合材料旋转梁的静、动态特性以及复合材料旋转梁不同铺层角、转速对固有频率的影响变化规律。在梁截面上设立翘曲节点引入翘曲变形,假设应变沿薄壁厚度呈二次曲线形式变化;由Hamilton原理,推导了复合材料梁的大变形公式;建立了考虑剪切、翘曲薄壁复合材料大变形梁静、动态分析的有限元模型,并编写了相应的计算程序。分析了复合材料薄壁梁大变形状态下的静态变形行为;在旋转状态下,考虑哥氏力影响,不同转速、不同铺层角对复合材料梁动态特性的影响。计算结果表明:能够用该文建立的模型计算复合材料梁的静动态特性,与相关文献计算结果进行比较,说明了模型的优越性。     

Warping torsion in thin-walled open section beams using the semiloof beam element

Many structural members including metallic, reinforced polymer and concrete members must be modelled, in the simplest approximation, as thin-walled beams whose cross-sections exhibit significant, out-of-plane warping owing to torsion. The elastic capabilities of the semiloof beam element are extended to include warping torsion of thin-walled open section beams. The performance of the extended element is compared with that of the original formulation.     

On the importance of cross-sectional warping in solid composite beams

The relative importance of the cross-sectional warping components in composite beams is studied and demonstrated using an exact solution for solid orthotropic beam of arbitrary cross-sectional geometry that undergoes a bending moment. In light of the effort required for warping modeling in general numerical schemes of composite beams, the present study contributes to the understanding of the importance of modeling the in-plane and the out-of-plane warping components.     

复合材料变截面旋转薄壁悬臂梁自由振动分析

基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。     

复合材料空间薄壁梁的有限元分析模型

在剪切梁理论的基础上, 采用9 节点平面单元模拟梁任意截面形状; 采用27 节点体单元, 模拟截面出平面外的二次翘曲位移, 从而建立了空间复合材料任意截面薄壁梁考虑二次翘曲的有限元分析模型。根据本文中导出的复合材料有限元模型编制了相应的分析计算程序。算例表明: 本文中建立的复合材料薄壁梁模型正确, 可以用于考虑多种耦合影响因素作用下复杂结构空间薄壁复合材料梁的有限元分析计算。      

A small strain,moderately large deflection finite element beam model with cross-sectional warping effect

A finite element model that can be applied to helicopter rotor blades has been developed with a particular emphasis on the proper representation of out-of-plane warping of arbitrary cross-sections. The model can describe accurately coupled bending, torsion and extensional behavior of beams undergoing small strain, moderately large deflection. The model can also handle beams with arbitrary cross-sections, taper, pretwist and planform. A main feature of the present approach is to introduce small warping displacement superimposed over flat cross-sections of a shear-flexible beam in the direction of the reference axis in deformed configuration. The nonlinear equilibrium equation resulting from finite element approximation is solved by the Newton-Raphson method. Numerical tests involving simple isotropic beams demonstrate the validity of the present approach.     

Investigation of composite box beam dynamics using a higher-order theory

A higher-order composite box beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.     

On the displacement formulation of torsion of shafts with rectangular cross-sections

The use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross-sections is studied. These functions can directly be employed in the displacement-based formulation of Hermitian and isoparametric three-dimensional beam elements for linear, elastic-plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.     

Investigation of composite ☐ beam dynamics using a higher-order theory

A higher-order composite ☐ beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.     

自然弯扭梁的耦合振动特性分析

以自然弯扭梁理论为基础对具有一般横截面形状空间曲梁的耦合振动特性进行了研究。 在该梁的运动控制方程中,位移函数和广义翘曲坐标均被定义在形心轴上,且在分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响。通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式,精确的固有频率则可用搜索的方法来确定。为了证明理论的有效性,对两端固支椭圆截面曲梁的固有频率和振型进行了求解,并把数值计算结果同使用PATRAN梁单元的有限元结果进行了比较。     

大挠度梁静态变形对动态特性影响分析

在经典梁理论基础上，引入剪切修正因子，采用U.L法，推导了新的空间大挠度梁的切线刚度矩阵；以三维连续体增量虚功原理为基础，建立了空间大挠度梁考虑剪切影响的静态分析模型和动态特性分析模型；首先根据所建立的模型进行了大挠度梁的静态特性分析，验证了模型的正确性；然后进行了大挠度梁的动态特性分析，揭示了悬臂梁静态大变形对动态特性的影响规律。指出悬臂梁在大载荷作用下，结构固有频率会因为梁的大变形而发生明显变化，基频变化尤为明显。     

非对称Bernoulli-Euler薄壁梁的弯扭耦合振动

通过直接求解均匀Bernoulli-Euler薄壁梁单元自由振动的控制运动微分方程,推导了其精确的动态传递矩阵。采用Bernoulli-Euler弯扭耦合梁理论,假定梁横截面没有任何对称性,考虑了薄壁梁在两个方向的弯曲振动及翘曲刚度的影响。动态传递矩阵可以用于计算非对称薄壁梁及其集合体的精确固有频率和模态形状。针对具体的算例,给出了各种边界条件下固有频率的数值结果并与文献中已有的结果进行了比较,还讨论了翘曲刚度对固有频率和模态形状的影响,结果表明如果忽略翘曲刚度的影响,可能得到毫无意义的结果。     

复合材料薄壁梁力学特性分析

综述了人们在建立研究复合材料薄壁梁力学特性的非线性梁理论及分析结构剖面特性,确立结构算子参数等方面所做的工作以及这些研究工作的特点。同时,结合作者的工作,介绍了近年来各国学者在复合材料薄壁梁力学特性研究上的进展。      

Investigation of Functionally Graded and Viscoelastic Layers Effects on the Dynamic Behavior of Functionally Graded Electro-Rheological Sandwich Beams

Vibration characteristics of functionally graded electro-rheological (FGER) sandwich beams are investigated. While a vast majority of studies have been reported about functionally graded material (FGM) or electrorheological fluids (ERF) composite beams, few, if any, works are conducted about FGER models. In order to validate the present finite element formulation of the FGER beam model, the results of the developed finite element (FE) model are compared with the results of an experimental test on a fabricated ERF composite beam. The effects of FGM volume fraction index, electric field, and thickness of the viscoelastic core are studied on the natural frequencies and modal loss factors of the FGER beam.     

A refined higher-order composite box beam theory

A three-dimensional theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Results presented for thick-walled box beams show the importance of including transverse shear in the formulation and the difficulty of defining a ‘beam’ twist for the entire cross-section.     

考虑滑移、剪力滞后和剪切变形的钢-混凝土组合梁解析解

通过在Newmark 模型中引入(1)描述横向非均匀分布的纵向位移的翘曲形函数和(2)描述钢梁腹板剪切变形的Timoshenko 梁假定,建立了一个能考虑滑移、剪力滞后和剪切变形的钢-混凝土组合梁模型,并推导了均布荷载作用下的解析解。最后通过4 个算例验证了模型和解析解的正确性和适用性,并显示了考虑组合梁剪切变形的必要性。另外,算例还表明,在组合梁的三维有限元建模中采用Timoshenko 梁单元来考虑钢梁的剪切变形会导致显著的误差。