On geometrically exact post-buckling of composite columns with interlayer slip—The partially composite elastica

This paper is focused on the geometrically exact elastic stability analysis of two interacting kinematically constrained, flexible columns. Possible applications are to partially composite or sandwich columns. A partially composite column composed of two inextensible elastically connected sub-columns is considered. Each sub-column is modeled by the Euler–Bernoulli beam theory and connected to each other via a linear constitutive law for the interlayer slip. The paper discusses the validity of parallel and translational kinematics beam assumptions with respect to the interlayer constraint. Buckling and post-buckling behavior of this structural system are studied for cantilever columns (clamped-free boundary conditions). A variational formulation is presented in order to derive relevant boundary conditions in a geometrically exact framework. The exact post-buckling behavior of this partially composite beam-column is investigated analytically and numerically. The Euler elastica problem is obtained in the case of non-composite action. The “partially composite elastica” is then treated analytically and numerically, for various values of the interaction connection parameter. An asymptotic expansion is performed to evaluate the symmetrical pitchfork bifurcation, and comparisons are made with some exact numerical results based on the numerical treatment of the non-linear boundary value problem. A boundary layer phenomenon, similar to that also observed for the linearized bending analysis of partially composite beams, is observed for large values of the connection parameter. This boundary layer phenomenon is investigated with a straightforward asymptotic expansion, that also is valid for large rotations. Finally, the paper analyses the effect of some additional imperfection eccentricities in the loading mode, that lead to some pre-bending phenomena.     

Variational base and solution strategies for non-linear force-based beam finite elements

This paper presents the variational bases for the non-linear force-based beam elements. The element state determination of these elements is obtained exactly from a two-field functional with independent stress and strain fields. The variational base of the non-linear force-based beam elements implemented in a general purpose displacement-based finite element program requires the inclusion of independent displacement field in the formulation. For this purpose, a three-field functional is considered with independent displacement, stress, and strain fields. Various local and global solution strategies come out from the mixed formulation of the beam element, and these are shown to yield the algorithms presented for non-linear force formulation beam elements in literature; thus removing any doubts on their variational bases. The presented numerical examples demonstrate the accuracy and robustness of the solution algorithms adapted for mixed formulation elements over popularly used displacement-based beam finite elements even for large structural systems.     

三维液体非线性晃动及其复杂现象

主要讨论三维液体非线性晃动问题 。将ALE（任意的拉格朗日-欧拉）运动学描述引人到Navier-Stokes方程的分步有限元计算格式中;在时间域上采用分步离散方法中的速度修正格式,利用Galerkin加权余量方法得到了系统的有限元离散方程;推导了考虑表面张力效应时有限元边界条件的弱积分形式;模拟了三维液体的非线性晃动问题,得到了一系列三维液体非线性晃动的复杂现象.进一步模拟了考虑表面张力效应以及在微重力环境下三维液体的非线性晃动,揭示了考虑表面张力效应以及在微重力环境下液体非线性晃动的重要特征.井将所得结论与现有的实验结果进行了比较.从而证实了该方法的有效性与正确性.     

基于离散元的杆件断裂全过程数值模拟

杆件的断裂会涉及到大变形、非线性以及不连续等问题,通常的数值计算方法模拟这种复杂力学行为具有局限性。本文基于颗粒离散元法DEM,将接触粘结处的分布式弹簧用梁纤维进行等效,提出了一种适于结构弹塑性分析的DEM纤维梁模型,然后在此基础上构建了构件断裂模拟算法以及纤维破环准则。将该模型应用于悬臂梁结构,模拟了悬臂梁从弹性到弹塑性阶段,再到断裂破坏的全过程,数值模拟得到的结构响应和截面开裂破坏形态均较合理。最后将该方法应用于单层网壳倒塌破坏模拟,并与网壳振动台倒塌试验进行对比,结果表明,数值模拟得到的杆件断裂过程及结构倒塌模式与试验现象一致,验证了该模型的正确性和适用性。     

悬索桥的非线性分析

为进行悬索桥的几何非线性分析，建立了梁单元的刚度矩阵及有关算法，通过算例验证了方法是可行的。     

Effects of Entropic Wave in Vibroacoustic Problem Using Boundary Element Analysis

A variational formulation for a vibroacoustic problem of a membrane and a viscothermal fluid is investigated in this paper. The formulation combines a variational formulation by integral equations of the fluid, that takes into account the acoustic and entropic waves coupling, with a variational formulation of the membrane. The formulation has been implemented numerically for the problems with axisymmetric geometry. The numerical results are compared to the analytical solution for a circular membrane coupled to a cylindrical cavity filled with air. These results show the validity of numerical implementation and illustrate the thermal effects of air on the membrane-cavity system modes in the micro cavities cases.     

Three-dimensional large deformation analysis of thin walled beams

A set of kinematic assumptions and constraints is used to develop a formulation for the analysis of thin-walled beams, of arbitrary open cross-section, subjected to arbitrarily large displacements in three-dimensional space. The validity of the formulation is illustrated through numerical solutions for elastic lateral-torsional post-buckling behavior of “I” beams, and a comparison of these solutions with experimental results.     

Light beams and radiation patterns in random media

The purpose of this paper is to apply a numerical technique in solving problems involving light beams in a random medium. The technique starts by generating numerically sample media with prescribed statistical properties. Rays are then traced in these sample media and the ray statistics are compiled. These statistics are utilized to find the mean square displacement and distribution of a beam. Problems on beam broadening and distortion of radiation patterns are considered. Fluctations in wave amplitude and phase are also investigated. When possible, the numerical results are compared with the analytical results and experimental results.It seems that the numerical technique has a potential to solve a great variety of problems. This is because it does not have severe restrictive conditions as those imposed on the analytic formulation. For example the technique is equally applicable when the irregularities are anisotropic, or when the background medium is inhomogeneous, or when the background is anistropic, or when there exist background wind. Some of these are discussed.     

Simulation of three-point bending at large deflections by an elastoplastic contact analysis

Three-point bending is simulated by an elaborate numerical procedure based on an elastoplastic, large deflection, contact analysis. A minimization formulation is used, which is equivalent to the incremental form posed as partial differential equations with inequalities. A sequential quadratic programming approach based on the finite-element technique is adopted as a method of solution. To examine the validity of the simulation method, experiments are carried out for specimens that have various widths.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Relaxed representations and improving stability in time-stepping analysis of three-dimensional structural nonlinear dynamics

In the present paper, we propose a representation of the discrete motion equations in structural nonlinear dynamics to obtain an improvement in the stability of time numerical integrations. A geometrically nonlinear total Lagrangian formulation for three-dimensional beam elements in the hypotheses of large rotations and small strains is presented. In this formulation, slopes are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. Such representations of the internal strains??rotations compatibility are then imposed in their time derivatives version. The results, related to Newmark approximations for the variations in the displacement and velocity vectors, show a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration steps. The numerical tests, furthermore, show that the variation in the total energy in the time steps has bounded oscillations about the zero value.     

A HIGH-ORDER RIGID-FLEXIBLE COUPLING MODEL OF A ROTATING FLEXIBLE BEAM UNDER LARGE DEFORMATION

对在平面内做大范围转动的中心刚体-柔性梁系统的刚柔耦合建模理论进行了深入研究,建立了系统的高次耦合动力学模型. 该动力学模型考虑了柔性梁横向弯曲变形和纵向伸长变形,且在纵向位移中计及由于横向变形而引起的纵向缩短项,即非线性耦合变形项,并保留了与非线性耦合项相关的一些高阶项,最终得到了系统的高次刚柔耦合动力学方程. 由此得到的动力学方程不仅能适用于柔性梁的小变形问题,也同样适用于大变形问题,弥补了一次近似耦合模型在处理柔性梁大变形问题上的不足. 通过与绝对节点坐标法以及一次近似耦合模型的对比验证了高次耦合模型的正确性.     

Static behavior and bifurcation of a monosymmetric open cross-section thin-walled beam: Numerical and experimental analysis

The aim of the paper is the numerical and experimental validation of a previously developed nonlinear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an open cross-section. Nonlinear in-plane and out-of-plane warping and torsional elongation effects are included in the model. To better understand the role of these new contributions a beam with a section with one symmetry axis, undergoing moderately large flexural curvatures and large torsional curvature is taken into account. To obtain a section of a cantilever beam for which the torsional curvature is expected to prevail with respect to the flexural ones, a preliminary study is performed. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of two different nonlinear finite element models and mainly with experimental results to confirm the validity of the analytical model. Interesting results are obtained for the critical values of the flexural–torsional instability loads.     

An improved dynamic model for a silicone material beam with large deformation

Dynamic modeling for incompressible hyperelastic materials with large deformation is an important issue in biomimetic applications. The previously proposed lower-order fully parameterized absolute nodal coordinate formulation (ANCF) beam element employs cubic interpolation in the longitudinal direction and linear interpolation in the transverse direction, whereas it cannot accurately describe the large bending deformation. On this account, a novel modeling method for studying the dynamic behavior of nonlinear materials is proposed in this paper. In this formulation, a higher-order beam element characterized by quadratic interpolation in the transverse directions is used in this investigation. Based on the Yeoh model and volumetric energy penalty function, the nonlinear elastic force matrices are derived within the ANCF framework. The feasibility and availability of the Yeoh model are verified through static experiment of nonlinear incompressible materials. Furthermore, dynamic simulation of a silicone cantilever beam under the gravity force is implemented to validate the superiority of the higher-order beam element. The simulation results obtained based on the Yeoh model by employing three different ANCF beam elements are compared with the result achieved from a commercial finite element package as the reference result. It is found that the results acquired utilizing a higher-order beam element are in good agreement with the reference results, while the results obtained using a lower-order beam element are different from the reference results. In addition, the stiffening problem caused by volumetric locking can be resolved effectively by applying a higher-order beam element. It is concluded that the proposed higher-order beam element formulation has satisfying accuracy in simulating dynamic motion process of the silicone beam.     

Modal Analysis of Monolithic and Jointed Type Cantilever Beams with Non-Uniform Section

Modal analysis of non-uniform bolted structures are of significance in modeling many complex mechanical structures. There are vast literatures available related with the analytical as well as numerical modeling of bolted joint. However, most of the analytical model discuss about the modeling of first mode of uniform structures with single bolted joint. In this paper, we present the modeling of single as well as bolted non-uniform beams using approximate mode shapes. To develop the model, we first carry out experiments to measures the modal frequencies and shapes of the test structures. Subsequently, we also do numerical modeling of non-uniform beams in ANSYS to verify the validity of the Euler-Bernoulli beam theory in developing the analytical models. Finally, using the Euler-Bernoulli beam theory, we obtain the analytical values of frequencies using the approximate the mode shapes. The analytical results are found to be closer to the experimental results with a maximum percentage error of about 15 %. The model presented in the paper can be extended to the mechanical structures with many non-uniform sections with or without bolted joints.     

作大范围回转运动柔性梁斜碰撞动力学研究

为正确估计由于碰撞引起的多柔体系统动力学特性的变化,针对作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,在考虑刚柔耦合效应的多柔体系统动力学建模理论的基础上,利用假设模态法建立起重力场作用下的柔性梁一致线性化动力法向碰撞过程中系统的动力行为。基于Ｈｅｒｔｚ接触理论和非线性阻尼项建立法向碰撞接触模型,基于线性切向接触刚度建立柔性梁切向碰撞接触模型,提出的数值算法保证了计算结果的合理性,给出的仿     

Trigonometric function used to formulate a multi-nodal finite tubular element

It is presented an alternative formulation to solve the problem of the deformation analysis for tubular element under pinching loads. The solution is based on a new displacement field defined from a total set of trigonometric functions. The solution is developed in a multi-nodal finite tubular ring element with a total of eight degrees of freedom per section considered. The purpose of this paper is to provide an easy alternative formulation when compared with a complex finite shell element or beam element analysis for the same application. Several case studies presented have been compared and discussed with numerical analyses results reported by other authors and the results obtained with a shell element from a Cosmos/M^® programme.     

Weak form quadrature element analysis of planar slender beams based on geometrically exact beam theory

This paper is devoted to the modeling of planar slender beams undergoing large displacements and finite rotations. Transverse shear deformation of beams that is trivial for most slender beams is neglected in the present model, though within the framework of the geometrically exact beam theory proposed by Reissner. A weak form quadrature element formulation is proposed which is characterized by highly efficient numerical integration and differentiation, thus minimizing the number of elements as well as the total degrees-of-freedom. Several typical examples are presented to demonstrate the effectiveness of the beam model and the weak form quadrature element formulation.     

On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load

The problem of a uniform cantilever beam under a tip-concentrated load, which rotates in relation with the tip-rotation of the beam, is studied in this paper. The formulation of the problem results in non-linear ordinary differential equations amenable to numerical integration. A relation is obtained for the applied tip-concentrated load in terms of the tip-angle of the beam. When the tip-concentrated load acts always normal to the undeformed axis of the beam (the rotation parameter, β=0) there is a possibility of obtaining non-unique solution for the applied load. This phenomenon is also observed for other rotation parameters less than unity. When the tip-concentrated load is acting normal to the deformed axis of the beam (β=1), many load parameters are obtained for a tip-angle with different deformed configurations of the beam. However, each load parameter corresponds to a tip-angle, which confirms the uniqueness on the solution of non-linear differential equations.