关于任意四边形截面柱体扭转问题

文献[1]提出通过一个映射变换来求解任意四边形截面柱体扭转问题,本文证明了这是不可能的,并且指出用类似的方法求解任意三角形截面柱体扭转问题也是不可能的.     

圓柱体具有圓弧裂縫的扭轉問題

设一圆柱体的圆截面,从该截面边界上任意两点出发,分别具有一条任意曲线形状的裂缝,如图1所示,对于这种一般性的裂缝圆截面的扭转问题,到目前还没有解决。在最简单的情况下,即从圆截面任意直径的两端出发,沿着直径的两条裂缝AP_1和CP_2(如图2所示)的扭转问题,在1942年威格尔斯沃斯得到了解决,但其裂缝AP_1和CP_2的长     

用伪应力函数法求解幂硬化材料柱体的扭转问题

本文引用伪应力函数使得幂硬化材料的任意形状等截面柱体和变直径圆截面柱体扭转问题的定解方程具有弹性柱体扭转问题的相应形式,从而可用类似于求解弹性柱体扭转的方法或直接利用已知的弹性解答求解对应的幂硬化材料柱体的扭转问题,本文用这种方法求得了幂硬化材料椭圆截面柱体及含球形空腔的圆轴扭转问题的解析解。     

用伪应力函数法求解幂硬化材料柱体的扭转问题

本文引用伪应力函数使得幂硬化材料的任意形状等截面柱体和变直径圆截面柱体扭转问题的定解方程具有弹性柱体扭转问题的相应形式,从而可用类似于求解弹性柱体扭转的方法或直接利用已知的弹性解答求解对应的幂硬化材料柱体的扭转问题,本文用这种方法求得了幂硬化材料椭圆截面柱体及含球形空腔的圆轴扭转问题的解析解。     

空间曲梁单元的扭转修正系数研究

三维空间曲梁有限单元模型是模拟曲梁结构的有效数值方法,可以考虑曲梁的弯扭耦合特性,最为符合曲梁的几何和受力特征.由于有限元法采用梁理论的平截面假定,空间曲梁单元上的扭转剪应力分布与实际曲梁截面上的扭转剪应力不同,从而会导致扭转刚度和扭转变形的计算失真.本文基于剪切应变能等效原理,推导了不同长宽比的矩形截面空间曲梁单元的扭转刚度修正系数η和截面边中点处扭转剪应力的修正系数λ,并采用曲线悬臂梁进行了验证.验证结果表明,根据本文提出的η作为校正因子的空间曲梁单元模型,对任意矩形截面曲梁计算的扭转变形均与实体单元模型的结果吻合良好;且只有截面为正方形时,扭转剪应力修正系数η才恰好与弯曲剪应力修正系数(1.2)一致.     

采用有限单元法计算梁任意形状截面特性

采用将梁截面离散化的方式,用数值积分计算截面的几何特性,并根据梁剪切变形和扭转理论,利用变分原理建立截面的有限元法方程,求解任意形状截面的扭转常数、剪切中心以及剪切面积修正系数等特性.本方法适用于各种形式的截面,具有计算精度高及适应性强的特点.根据上述理论编制了相应程序,按照不同的单元划分方式,分别计算出矩形截面截面特性,与理论解进行比较;又对舟山市定海长峙至岙山预应力混凝土连续箱梁截面进行了计算,并与Ansys结果进行比较,均证明采用本文的计算方法能得到满意的结果,且该方法适用于各种形状的截面形式.     

偏压薄壁杆稳定计算的有限杆元法

根据能量原理,综合三次B样条函数、有限单元法和经典Vlasov薄壁杆理论的优点,提出偏压薄壁杆稳定计算的有限杆元法．推导和求解过程中,同时考虑了截面扭转、翘曲和杆中面上剪应变的影响,可适用求解常用边界条件,任意截面形状的薄壁杆特征值问题．与经典方法比较显示着该文计算方法的有效性．     

圆截面弹性细杆的平面振动

基于Kirchhoff理论讨论圆截面弹性细杆的平面振动．以杆中心线的Frenet坐标系为参考系建立动力学方程．杆作平面运动时，其扭转振动与弯曲振动解耦．讨论任意形状杆的扭转振动和轴向受压直杆在无扭转条件下的弯曲振动，证明直杆平衡的静态Lyapunov稳定性与欧拉稳定性条件为动态稳定性的必要条件．考虑轴向力和截面转动惯性效应的影响，导出弯曲振动的固有频率．     

粘性不可压缩流体定常层流管流及柱体的扭转

本文用加权残数法求得了任意等腰三角形及矩形截面的柱体的扭转问题以及和柱体形状相同的等截面长管的不可压缩粘性流体的定常层流问题的近似解.近似解有较高的精确度.另外,文中还提出了变率配域法的概念.     

任意四边形截面直杆扭转问题的简易解法

本文采用一个简单的映射变换,将任意四边形映射为正方形,利用文[2]的结果,得到任意四边形截面直杆扭转的一种简单的半解析解法。     

混凝土结构扭转理论研究的进展

本文回顾了国内外混凝土结构扭转理论的历史发展,尤其是最近十几年来的进展。文中就有代表性的斜弯理论和空间桁架理论进行了述评。并按照结构构件受纯扭、弯扭及弯剪扭联合作用等加载方式,对于素混凝土、钢筋混凝土和预应力混凝土结构扭转的计算方法进行了归纳。最后对我国开展混凝土结构扭转理论的研究提出了建议。      

Evaluation of multiaxial theories for room-temperature plasticity and elevated-temperature creep and relaxation of several metals

Based on the assumption that the material satisfies the condition of isotropic hardening for either a von Mises or a Tresca material, finite-strain theories are derived for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent. In the latter case, both creep and relaxation theories are derived. At room temperature the theories are evaluated for each of eight metals using finite-strain data from tension, compression and torsion members. Of the six metals that are found to satisfy the condition required for the isotropic-hardening model, two are von Mises, one is Tresca, and the other three are between von Mises and Tresca. At elevated temperatures, the theories are evaluated for each of five of the latter six metals, using data from tension and torsion members. Material properties obtained from the tension specimens are used to predict creep and relaxation curves for the torsion members. Contrary to the results at room temperature, creep curves for the torsion members do not all fall within the region bounded by von Mises and Tresca theories. In the case of relaxation, either excellent agreement is obtained between the von Mises strain-hardening theory and experimental data or the theory is conservative.     

Second-order torsion problem of a homogeneous isotropic compressible multiply-connected elastic cylinder

For simply-connected regions, some solutions are available for the second-order torsion problem of homogeneous isotropic compressible elastic cylinders based on the theory given by Green and others. In the present paper, these theories are extended to cover the second-order torsion problem for multiply-connected regions. As an example, results for torsion of a confocal elliptical ring are given.     

Evaluation of finite-plasticity theories for torsion-tension members made of tresca materials

Finite-incremental Tresca and von Mises theories are developed for solid circular-section torsion-tension members subjected to proportionate and nonproportionate loading. The materials are assumed to be isotropic and even. Two Tresca theories and a von Mises theory are compared with test data obtained from torsion-tension members. Three different kinds of steels were tested; they are hot-rolled mild steel, annealed mild steel, and hot-rolled SAE 1017 steel. The fully plastic values of axial load and torque predicted by the Tresca theories agree with the experimental results; however, the deformations, in the strain-hardening region, predicted by both of the Tresca theories were greater than observed. The von Mises theory is nonconservative in predicting the fully plastic loads of torsion members and torsion-tension members and in predicting the deformations of torsion members in the strain-hardening region, but gives good correlation between predicted and experimental deformations for the torsion-tension members in the strain-hardening region.     

Second-order torsion problem of a cylinder consisting of different isotropic homogeneous compressible elastic materials

Some second-order solutions of the torsion problem for simply-connected regions are available based on the theory given by Green and others both for compressible and incompressible materials. Bhargava and Gupta [1] have recently extended the theory for torsion problem of multiply-connected regions. In the present paper these theories are extended further to account for the composite regions. The complex variable formulation is employed. As an illustration, results for the torsion problem of a composite cylinder of concentric circular cross-section are given.     

Strain gradient elasticity and stress fibers

Since stress fibers have micro-size dimensions, their biomechanical behavior should demand mechanical models conforming with gradient strain deformation theories. In particular, the torsion and the stretching of stress fibers are discussed into the context of strain gradient elasticity theory and their size effects. It is proven for the torsion problem that the torsion moment varies with the axial length of the bar for constant twist angle, whereas for the simple tension problem, the strain is non-uniform along the stress fiber. The proposed theory is supported by experimental evidence.     

Torsion of thin tubes: A justification of some classical results

In this paper we study the Sain-Venant torsion problem for hollow homogeneous isotropic cylinders with thin doubly connected cross-section. By using the framework of the -convergence of functionals, the classical theories of Bredt and of the sectorial areas are shown to be the variational limit of the torsion problem for cylinders with a hollow cross-section of vanishing thickness.     

A relook at Reissner’s theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.     

Non-uniform warping including the effects of torsion and shear forces. Part II: Analytical and numerical applications

This two-part contribution presents a beam theory (BT) with a non-uniform warping (NUW) including the effects of torsion, and shear forces and valid for any homogeneous cross-section made of isotropic elastic material. In part I, the governing equations of the NUW-BT has been established and simplified-NUW-BT versions has been deduced, wherein the number of degrees of freedom is reduced. In this part II, these theories are used to analyze, for a representative set of cross-sections (CS) (solid-CS and thin-walled open/closed-CS, bi-symmetric or not), the elastic behavior of cantilever beams subjected to torsion or shear-bending. For bi-symmetrical-CS, torsion and shear-bending are analyzed separately: analytical and numerical results are given for the distributions along the beam axis of the cross-sectional displacements and stresses, for the NUW-BT and its simplified versions. Numerical results are also given for the three-dimensional stress distributions close to the embedded section: the stress predictions of the NUW-BT are compared to those obtained by three-dimensional finite elements computations. It can be drawn from all these results indications that can help to decide when the simplified theories may be applied, and hence when the warping parameters may be reduced. As specified in NUW-BT, torsion and bending are coupled for non-symmetrical-CS, even if the bending moments refer to the centroid while the torsional moment refers to the shear center. To illustrate this coupling effect, the particular example of the channel-CS presented in Kim and Kim [Kim, N.-I., Kim, M.-Y., 2005. Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects. Thin-Walled Structures 43, 701–734.] is analyzed and the results are compared.     

On the Problem of Torsion in Finite Elasticity:Part I,The General Formulation in the Case of Torsion with Variable Twist

ABSTRACT

The problem of nonuniform torsion of beams with solid cross-sections is examined in the finite displacement theory of elasticity. Two approximate theories are formulated by applying Reissner's theorem for finite elastic deformations. A perturbation solution scheme is presented, to study results implied by the two approximate formulations.