Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element method.Based on the first-order shear deformation theory(FSDT),the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type.A C^0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations.By adopting the extended rule of mixture,the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters.Four carbon nanotube(CNT)distributions,labeled uniformly distributed(UD)-CNT,FG-VCNT,FG-O-CNT,and FG-X-CNT,are considered.The solution procedure is carried out via the Newton-Raphson incremental technique.Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model.The effects of the CNT distributions,their volume fractions,and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

Analytic Static Deflection Solutions of Uniform Cantilever Beams Resting on Nonlinear Elastic Rotational Boundary

In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.

Simulation of Steel Reinforcement on the Nonlinear Behaviour of Slender Glulam Beam Columns by Using the Newton-Raphson Method

The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

In this paper, exact solutions of large deflection of multilayer sandwich shallow shellsunder transverse forces and different boundary conditions are presented. Exact results ofpostbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlineardeflection of general shallow shells such as spherical shells under inplane edge forcesare also obtained by the same procedure.

DIFFERENTIAL QUADRATURE FOR AXISYMMETRIC GEOMETRICALLY NONLINEAR ANALYSIS OF CIRCULAR PLATES

New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.

Large deflection of curved elastic beams made of Ludwick type material

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlin- earities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

VIBRATION PROBLEMS OF FLEXIBLE CIRCULAR PLATES WITH INITIAL DEFLECTION

In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

Large Deflection Dynamic Response Analysis of Flexible Hull Beams by the Multibody System Method

In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.

A Comparative Study on the Flexural Behaviour of Waffle and Solid Slab Models When Subjected to Point Load

The determinations of flexural behavior of some engineering structures are based on different theories and equations, but it has been observed that some of these equations may not give true representation. This work has looked into the difference that may occur between theoretical and experimental results. An experimental test carried out on models of waffle and solid slabs structures were described and results from twenty test samples are presented. Each specimen was subjected to an incremental axial loading of 1 kN interval after 28 days of casting. The flexural moments, deflections and crack width at failure were obtained. The experimental flexural crack and theoretical flexural cracks for both types of slabs were compared. The result for flexural moments for waffle was 5.526 kNm, while solid slab was 3.684 kNm. The deflections showed that waffle slabs has 3.64 mm while solid has 9.28 mm, hence waffle has a higher structural stiffness than solid slabs, but the flexural cracks did not give the same results especially for the estimated crack width. It was concluded that estimated results based on developed equations may not be accurate because it is based on ideal situation.

New nonlinear stiffness actuator with predefined torque‒deflection profile

A nonlinear stiffness actuator(NSA)could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range,both of which are beneficial for physical interaction between a robot and the environment.Currently,most of NSAs are complex and hardly used for engineering.In this paper,oriented to engineering applications,a new simple NSA was proposed,mainly including leaf springs and especially designed cams,which could perform a predefined relationship between torque and deflection.The new NSA has a compact structure,and it is lightweight,both of which are also beneficial for its practical application.An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed.The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring.Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism,the sliding displacement between the cam and the leaf spring is very small,and consumption of sliding friction force is very low.Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles.Three kinds of prototype experiments,including verification experiment of the predefined torque‒deflection profile,torque tracking experiment,and position tracking experiment under different loads,were conducted.The results prove the accuracy of performing the predefined torque‒deflection profile,the tracking performance,and the interactive performance of the new NSA.

NONLINEAR FLEXURAL WAVES IN LARGE-DEFLECTION BEAMS

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m→1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.

Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode

The nonlinear behaviors of a circular-cylinder piezoelectric power harvester （CCPPH） near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large defection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multi- valuedness and jump behaviors.

NONLINEAR DEFORMATION THEORY OF THIN SHELL

The exact relation between strain and displacement is given for nonlinear deformation of thin shell. The! fundamental formula of large deformation when the deflection is on the same class with the thickness of the shell is derived after simplified rationally. The fundamental formula of large deformation when the deflection is art the same class with the length of the shell is derived exactly for cylinder shell deformed cylindrical shaped.

Deflection amplification factor for estimating seismic lateral deformations of RC frames

Different values have been assigned to the ratio of the defl ection amplifi cation factor(Cd) to the response modifi cation factor(R) for a specifi ed force-resisting system in the seismic design provisions while the same application is defi ned for it. An analytical study of the seismic responses of several reinforced concrete frames subjected to a suite of earthquake records performed in this research indicate that the stories’ overstrength and stiffness distribution along the structural height can affect local defl ections more than global ones. Therefore, the Cd/R ratio is calculated based on the ratio of both maximum inelastic to maximum elastic displacements and interstory drifts. Due to damage concentration in some specifi c stories, the defl ection amplifi cation factor calculated based on inelastic interstory drifts was larger than that of the inelastic displacements. Consequently, a minimum value of 1.0 is recommended for the Cd/R ratio in order to estimate maximum inelastic drifts. The ratio of inelastic to elastic displacement was generally found to increase slightly along the structural height for the studied RC models. In addition, it was detected that the story damage indices of the studied RC frames decrease when the inverted value of inelastic interstory drift ratios are increased through a(negative) power form.

Experimental and Numerical Investigations of the Hydrodynamic Characteristics, Twine Deformation, and Flow Field Around the Netting Structure Composed of Two Types of Twine Materials for Midwater Trawls

Nettings are complex flexible structures used in various fisheries.Understanding the hydrodynamic characteristics,de-formation,and the flow field around nettings is important to design successful fishing gear.This study investigated the hydrodynamic characteristics and deformation of five nettings made of polyethylene and nylon materials in different attack angles through numeri-cal simulation and physical model experiment.The numerical model was based on the one-way coupling between computational fluid dynamics(CFD)and large deflection nonlinear structural models.Navier-Stokes equations were solved using the finite volume ap-proach,the flow was described using the k-ωshear stress turbulent model,and the large deflection structural dynamic equation was derived using a finite element approach to understand the netting deformation and nodal displacement.The porous media model was chosen to model the nettings in the CFD solver.Numerical data were compared with the experimental results of the physical model to validate the numerical models.Results showed that the numerical data were compatible with the experimental data with an average relative error of 2.34%,3.40%,6.50%,and 5.80%in the normal drag coefficients,parallel drag coefficients,inclined drag coefficients,and inclined lift coefficients,respectively.The hydrodynamic forces of the polyethylene and nylon nettings decreased by approxi-mately 52.56%and 66.66%,respectively,with decreasing net solidity.The drag and lift coefficients of the nylon netting were appro-ximately 17.15%and 6.72%lower than those of the polyethylene netting.A spatial development of turbulent flow occurred around the netting because of the netting wake.However,the flow velocity reduction downstream from the netting in the wake region in-creased with increasing attack angle and net solidity.In addition,the deformation,stress,and strain on each netting increased with in-creasing solidity ratio.

周边简支双向密肋楼盖非线性分析

选用通用有限元分析软件ANSYS中的混凝土实体单元SOLID65对周边简支双向密肋楼盖进行了试验模拟。编写了钢筋混凝土楼板的APDL语言分析程序,并对密肋楼盖进行了非线性全过程分析。将数值解与试验结果中的极限荷载、最大应力值和荷载-位移曲线进行了比较分析。在权衡了计算精度与计算机时之间矛盾的基础上,总结了该有限元模型的数值模拟结果与试验结果吻合较好,从而验证了钢筋混凝土楼盖结构应用实体单元进行非线性有限元分析的合理性。

大挠度索结构的非线性有限元分析

本文基于有限元理论，将大挠度索离散为一系列小挠度索单元，推导出索结构的刚 度矩阵的显式。应用本文介绍的方法，可以计算任意挠度、作用有任意荷载的索结构。经过 算例对比，表明本文方法对于求解索结构是一种很好的方法。

斜尖针穿刺软组织建模及针尖轨迹预测

在经皮穿刺过程中,当带斜尖的针穿刺软组织时,针与其周围组织相互作用,导致针体产生弯曲变形,针尖偏离预定方向,进而直接影响穿刺手术的定位精度。将针穿刺软组织的过程视为准静态过程,并进行离散化,建立针-组织相互作用模型。在该模型中,考虑到软组织的非线性与各向异性,将针视为由一系列非线性弹簧支撑的悬臂梁,且各点的弹簧刚度彼此不同。建立针-组织相互作用中的摩擦力及切割力模型,借助于穿刺实验,将穿刺力分解为摩擦力和切割力,进而获得力模型中的各个参数。基于虚拟非线性弹簧模型和穿刺力模型,根据最小势能原理,采用瑞利-里兹法预测针的偏转,进而获得进针过程中针尖的轨迹。仿真及实验结果表明,该模型能够精确地预测针尖位置,为穿刺路径规划提供理论依据。