Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula

Fractional order models of a spring/spring-pot and spring/spring-pot/actuator element connected into a multibody system are proposed in order to represent smart materials and components in adaptronic systems by introducing new tuning parameter. The models are introduced into dynamic equations via generalized forces and using the Lagrange's equations of the second kind in covariant form. Generalized forces are derived by taking into account fractional order derivatives in force–displacement relations and by using the principle of virtual work. The numerical scheme for solving fractional order differential equations proposed in Atanacković and Stanković (2008) is used in order to approximate fractional order derivative of a composite function appearing in the presented fractional order model. Numerical example for the multibody system with three degrees of freedom is presented. The results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model.     

Effective and efficient characterization of lubrication flow over soft coatings

This work models the fluid-structure interactions associated with separating a solid from a soft elastic film in a liquid environment. One side of the soft film is permanently attached to a rigid substrate. The ensuing liquid flow and elastic deformations are derived by considering a system of partial differential equations, that govern the mechanics of the separation process. A finite element based computational scheme is developed to solve the governing equations and predict the resultant forces acting on the solid. It is shown that the resulting forces are influenced by the elasticity of the film for an initial duration and by the viscosity of the liquid at larger times. The proposed model is utilized to shed insights into the mechanics of the separation process in constrained-surface stereolithography process.

     

A general failure criterion for spot welds under combined loading conditions

The circumferential failure mode of spot welds is investigated under combined loading conditions. Failure mechanisms of spot welds under different loading conditions are first examined by the experimental observations and a plane stress finite element analysis. An approximate limit load analysis for spot welds is then conducted to understand the failure loads of spot welds under combinations of resultant forces and resultant moments with consideration of the global equilibrium conditions only. The approximate limit load solution for circumferential failure is expressed in terms of sheet thickness, nugget diameter and combinations of loads. Failure contours are generated for spot welds under opening and shear loading conditions. The results indicate that failure contours become smaller when the ratio of the sheet thickness to the nugget diameter increases. Based on the approximate limit load solution, a general quadratic failure criterion for spot welds under combined three resultant forces and three resultant moments is proposed with correction factors determined by fitting to the experimental results of spot welds under combined loading conditions. The failure criterion can be used to characterize the failure loads of spot welds with consideration of the effects of sheet thickness, nugget diameter and combinations of loads. Experimental spot weld failure loads under combined opening and shear loading conditions and those under combined shear and twisting loading conditions are shown to be characterized well by the proposed failure criterion. Finally, a simplified general failure criterion for spot welds under three resultant forces and three resultant moments is proposed by neglecting the coupling terms of the resultant forces and moments for convenient use of the failure criterion for engineering applications.     

空间结构支座摩擦力问题的研究

本文根据力学概念和库仑摩擦定律,建立了空间结构支座摩擦力问题的精确数学模型并提出了两种解法,即数学规划法和弹簧约束法;同时指出了考虑支座摩擦力作用的结构分析方法。算例表明本文的方法是很有效的。本文的研究成果已应用于实际工程的结构优化设计。     

双拉试样裂纹扩展过程中的应力强度因子计算

论文将使用一种界面单元来解决二维裂纹的静态扩展问题.这种界面单元基于虚拟裂纹闭合法,利用商业有限元软件ABAQUS的用户自定义单元UEL功能,发展为界面断裂单元,计算应变能释放率(GⅠ和GⅡ).在裂纹尖端的两个节点间设置一个特殊刚度的弹簧,并引入哑节点计算裂纹尖端后面的张开位移和裂纹尖端前面的虚拟裂纹扩展量.采用这种单元计算应变能释放率时不需要使用奇异单元或折叠单元,不会出现收敛问题,也不需要复杂的后续处理.因此,采用这种断裂单元分析二维裂纹扩展问题是方便的、高效率的,而且也能得到可靠的精度.     

Buckling behavior of perfect and defective DWCNTs under axial, bending and torsional loadings via a structural mechanics approach

The buckling behavior of perfect and defective double-walled carbon nanotubes (DWCNTs) under axial compressive, torsional and bending loadings is investigated using a structural mechanics model. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element. Critical buckling loads, critical buckling moments and the effects of vacancy defects were studied for armchair nanotubes with various aspect ratios. The results show that vacancy defects greatly reduce the critical buckling load of DWCNTs. The density of defects plays an important role in buckling of DWCNTs. The results of this numerical model are in good agreement with their comparable existing works.     

A non-linear 3-D finite element analysis of soil failure with tillage tools

A non-linear 3-D finite element model was developed to study the soil failure under a narrow tillage blade. The weighted residual method was applied to formulate the finite element model. The Duncan and Chang hyperbolic stress-strain model was used in the analysis. This finite element model also takes into account friction at the soil-tool interface, and progressive and continuous cutting. A FORTRAN program was written to carry out the finite element analysis. The results provided soil forces, a progressive developed failure zone, displacement field and stress distribution along the tool surface. Tillage were conducted in the laboratory soil bin to verify soil forces from the finite element analysis. The comparison between the results from the finite element model and those from the soil bin tests was reasonably good.     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reflect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.     

Buckling load and critical length of nanowires on an elastic substrate

This paper considers the stability of nanowires on an elastic substrate. The problem is converted to a generalized Euler problem containing rotational spring restraint. When distributed loading and tip forces are simultaneously applied, the buckling problem of a heavy nanocolumn with rotational spring junction is reduced to an integral equation. An approximate buckling load equation is derived explicitly. The critical length of nanocantilevers is given in closed form. Results indicate that spring stiffness increases the critical length of nanowires. The effect of self-weight on the critical length is pronounced for small tip forces, and becomes weaker for larger tip forces.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.     

基于离散模型的混凝土构件破坏过程研究

刚体-弹簧元模型是一种离散化分析模型,可以反映连续体从开裂到破坏不连续过程的真实裂缝形态。本文在总结既有相关研究的基础上,引入并程序化刚体-弹簧元模型用于混凝土构件开裂破坏行为研究,特别是有关混凝土构件开裂后直至破坏的裂缝真实形态研究。首先确定了三维刚体-弹簧元模型中刚体单元的划分、弹簧元的特性（混凝土材料本构关系施加于弹簧元）、刚体单元与弹簧元装配方式、钢筋本构关系及其与混凝土相互作用,然后实现了刚体-弹簧元模型用于混凝土构件开裂破坏行为研究的程序化,并以剪切破坏的钢筋混凝土构件进行实例验证。结果表明,基于刚体-弹簧元模型的程序可以较为准确地反映该钢筋混凝土构件从开裂到破坏真实裂缝形态。     

The characteristics of soil reaction forces on a single movable lug

In order to understand clearly the characteristics of the soil reaction forces on a single movable lug, the resultant of measured soil reaction forces was determined and presented along with its position on the lug plate. The resultant of soil reaction forces acting on the movable lug increased gradually and reached the maximum value when the lug was on about its lowest position in the soil, then it decreased without offering any downward resistance to the lug till the lug left the soil. The maximum resultant force of the movable lug was higher than that of a fixed lug. The point of action of the resultant force on the movable lug shifted in a similar way in all test cases, that is, it moves to the center of the lug from the outer tip until it reaches the position where it becomes the maximum, then it moves to the outer tip till the lug leaves the soil. The inclination angle of the resultant force increased with the decrease of lug inclination angle. The bigger lug sinkage of the movable lug produced bigger soil reaction forces and shifted the point of action of the resultant force from the tip part to the central part of the lug. However, there was no significant effect of the lug sinkage on the direction of the resultant force. The increase in lug slippage from 25% to 50% brought bigger soil reaction forces on the movable lug, but did not influence the direction and point of action of the resultant force.     

变形能分解的新概念与圣维南原理

在小变形情况下分析了三维各向异性弹塑性体当表面小区域受载时的变形能，所得表达式的每一项都具有明确的物理意义，能清晰地显示出载荷的各特征因素对变形能的贡献，文中提出的有关变形能分解的新概念对于揭示圣维南原理所描述现象的力学机理具有重要意义。     

Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.     

一种滞弹簧耗能的新型离散元滚动阻力模型研究

颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.      

简化有限元方法的波纹管模态分析

采用简化方法对单层U型波纹管进行有限元模态分析。在长度,质量,对轴线转动惯量,体积,轴向弹簧比率以及周向弹簧比率不变的前提下,把波纹管简化成直壁薄管,用直壁薄管模型代替波纹管模型进行有限元模态计算。简化了计算模型,减少了计算量,提高了计算效率。本文给出了明确的等效直壁薄管的几何参数,物性参数的求解公式,改变了Broman人为设定直壁薄管厚度的方法,取得了更加准确的计算结果,使利用直壁薄管模型求解波纹管固有频率具有通用意义。进行了直壁薄管模型得到模态振型与波纹管模型得到模态振型之间的比较,认为直壁薄管模型可以求解波纹管的振型。