COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD

The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.

A Comparative Study on the Truck Frame Stiffness with Solid and Beam Element FEA Models

Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Ultrasonic beam steering using Neumann boundary condition in multiplysics

The traditional one-dimensional ultrasonic beam steering has time delay and is thus a complicated problem. A numerical model of ultrasonic beam steering using Neumann boundary condition in multiplysics is presented in the present paper. This model is based on the discrete wave number method that has been proved theoretically to satisfy the continuous conditions. The propagating angle of novel model is a function of the distance instead of the time domain. The propagating wave fronts at desired angles are simulated with the single line sources for plane wave. The result indicates that any beam angle can be steered by discrete line elements resources without any time delay.

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.

A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

THE CURVED BEAM ELEMENT AND ITS CONVERGENCE RATE

The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam clement. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approxtmately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l2) and when regular elements are used. I is the element length.

A method for generating double-ring-shaped vector beams

We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam–Berry phase（PBP） optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases.

A three-dimensional nonlinear reduced-order predictive joint model

Mechanical joints can have significant effects on the dynamics of assembled structures.However,the lack of efficacious predictive dynamic models tot joints hinders accurate prediction of their dynamic behavior.The goal of our work is to develop physics-based,reduced-order,finite element models that are capable of replicating the effects of joints on vi- brating structures.The authors recently developed the so-called two-dimensional adjusted lwan beam element(2-D AIBE) to simulate the hysteretic behavior of bolted joints in 2-D beam structures.In this paper,2-D AIBE is extended to three-di- mensional cases by formulating a three-dimensional adjusted lwan beam element(3-D AIBE).hupulsive loading experi- ments are applied to a jointed frame structure and a beam structure containing the same joint.The frame is subjected to ex- citation out of plane so that the joint is under rotation and single axis bending.By assuming that the rotation in the joint is linear elastic,the parameters of the joint associated with bending in the flame are identified from acceleration responses of the jointed beam structure,using a multi-layer teed-torward neural network(MLFF).Numerieal simulation is then per- formed on the frame structure using the identified parameters.The good agreement between the simulated and experimental impulsive acceleration responses of the frame structure validates the efficacy of the presented 3-D AIBE,and indicates that the model can potentially be applied to more complex structural systems with joint parameters identified from a relatively simple structure.

Influential Factors in Safety Design of Aircraft Pneumatic Duct System

The reliability and safety of the pneumatic ducts are essential for flight safety.A beam element model of the duct system is developed and the factors that impact the stress performance of the duct system are investigated,such as stress check standards,flight acceleration,internal temperature and internal pressure.The results show that the stress synthetic method as the stress check standard can obtain the more safety design results.The maximum stress of straight pipe is affected significantly by the acceleration in a plane perpendicular to straight pipe,while the maximum stress of bend pipe is greatly affected by the acceleration in the direction perpendicular to plane of the bend pipe.Meanwhile,internal pressure has little effect on the maximum stress of bend pipe and straight pipe.Temperature has little effect on the maximum stress of bend pipe while has a big impact on the maximum stress of straight pipe.

Seismic elastic-plastic time history analysis and reliability study of quayside container crane

Quayside container crane is a kind of huge dimension steel structure,which is the major equipment used for handling container at modern ports.With the aim to validate the safety and reliability of the crane under seismic loads,besides conventional analysis,elastic-plastic time history analysis under rare seismic intensity is carried out.An ideal finite element（FEM） elastic-plastic mechanical model of the quayside container crane is presented by using ANSYS codes.Furthermore,according to elastic-plastic time history analysis theory,deformation,stress and damage pattern of the structure under rare seismic intensity are investigated.Based on the above analysis,the established reliability model according to the reliability theory,together with seismic reliability analysis based on Monte-Carlo simulation is applied to practical analysis.The results show that the overall structure of the quayside container crane is generally unstable under rare seismic intensity,and the structure needs to be reinforced.

Laser beam characteristic for laser resonators with diffraction optical elements

The matrix eigenvalue method is used to analyze a laser resonator composed of diffraction optical elements. The results show that this type of resonator can separate fundamental mode and high order modes effectively. The output beams can be designed for different requests.

Equivalent Simplifying of Tower Structure and Its Application in Overall Analysis of Offshore Platform

Based on some mechanical principles, this paper presents a new way for simplifying the tower structure on the platform, i. e., substituting the three-dimensional tower structure by using beam elements. For the overall analysis of offshore platform, this method can not only save man- power and computer time, but also get better results. This paper introduces the equivalent-simplifying method and its application in engineering.

Two-Layer Contact Nonlinear Mechanical Analysis of Flexible Drilling Tool in the Wellbore

The lack of research on flexible drilling tool leads to limited application of ultra-short radius horizontal wells.The flexible drilling tool is different from the conventional drilling tool.The flexible drilling pipe involves a mutual transition between the structure and the mechanism during the deformation process.At the same time,the flexible drilling pipe and the eccentric guide tube,the guide tube and the wellbore generate random contact.In this paper,3-D beam elements,universal joint elements,rigid beam elements and the beam-beam contact elements are combined to establish a two-layer contact nonlinear finite element model of the flexible drilling tool in the wellbore.The dynamic relaxation method is introduced for numerical solution.The feasibility of the model and the algorithm is verified by an example.The mechanical analysis of flexible drilling tool under the four hole inclinations in the oblique section is carried out.It is found that the flexible drilling pipe has a“folded line”deformation.The contact force between the flexible drilling pipe and the guide tube is randomly distributed.The contact force between the guide tube and the wellbore in the oblique section is greater than that in the vertical section.As the hole inclinations increase,the torque and axial force transmitted to the drill bit gradually decrease.

Fracture Behavior of Epoxy Asphalt Pavement on Steel Bridges based on Optical Fiber Sensing Technology and Numerical Simulation

The distributed optical fiber sensing technology was used to investigate the fracture behavior of the Epoxy Asphalt Mixture. The spatial distribution and variation of the strain development with crack propagation were acquired using the brillouin optical time-domain reflectometer through the loading experiments of the composite beam structure. In addition, a finite element model of the composite beam structure was developed to analyze the mechanical responses of the epoxy asphalt mixture using the extended finite element method. The experimental results show that the development of crack propagation becomes instable with the increase of the load, and larger loads will generate deeper cracks. Moreover, the numerical results show that the mechanical response of the crack tip changes with the crack propagation, and the worst areas that subjected to crack damage are located on both sides of the composite beam structure.

Light weight analysis of a skeleton vehicle frame using BS960 super-high-strength steel

Static strength finite element analysis was conducted to decrease the weight of a skeleton vehicle＇s frame. Results indicated that the maximum stress occurs on the front beam ＇s variable section area. Dynamic sensitivity analysis elucidated the relationship between the maximum stress and the thickness of a particular beam,e. g.,top,middle,and bottom beam. Displacement was analyzed by the key part that influenced the maximum stress. Finally,the new plan using BS960 super-high-strength beam steel and the preferred beam thickness was compared with the original plan. New combinations of beam thickness were introduced on the basis of different purposes; the maximum responding light w eight ratio was 21%.