Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

MIXED ENERGY METHOD FOR SOLUTION OF QUADRATIC PROGRAMMING PROBLEMS AND ELASTIC-PLASTIC ANALYSIS OF TRUSS STRUCTURES

A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method proposed is different from the traditionalone, for which the unknown variables are selected just in one classsuch as displacements or stresses. The present method selects thevariables in the mixed form with both displacement and stress. As themethod is established in the hybrid space, the information found inthe previous incremental step can be used for the solution of thepresent step, making the algorithm highly effi- cient in thenumerical solution process of quadratic programming problems. Theresults obtained in the exm- ples of the elastic-plastic solution ofthe truss structures verify what has been predicted in thetheoretical anal- ysis.

Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

Mechanical analysis of double-layered circular graphene sheets as building material embedded in an elastic medium

Possessing the unique and highly valuable properties, graphene sheets(GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concrete and other building materials. In this work, the nonlocal elastic theory and classical plate theory(CLPT) are used to derive the governing equations. The element-free framework for analyzing the buckling behaviors of double layer circular graphene sheets(DLCGSs) relying on an elastic medium is proposed. Pasternak-type model is adopted to describe the elastic medium. Accordingly, the influences of boundary conditions, size of GSs and nonlocal parameters on the buckling behavior of DLCGSs are investigated. The results show that the OP buckling modes are only sensible to the van der Waals forces.

Nonlinear dynamic analysis on rigid-flexible coupling system of an elastic beam

Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.

Analysis and interpretation on the concrete quality of shaft lining by elastic wave technique

The quality problem of the concrete body and backwall grouting of shaft lining must be taken into consideration during the engineering construction of the shaft. Detection and evaluation are needed to determine the parameters such as the location and depth of drilling. The record of elastic wave can be gained through laying the surveying lines of the ring and ver- tical direction in the shaft lining by the elastic wave method. And specifically, through analyzing the different parameters of seismic attribute such as the velocity of high frequency reflection wave, amplitude and frequency, the abnormal range on the wall or under the wall can be forecasted. The concrete quality of shallow layer in the shaft lining can be evaluated through the velocity of surfer wave. Using the evaluating technique of comprehensive frequency and the phase feature of waveform, the basic features such as inner construction, wall back filling and failure depth of shaft lining can be interpreted from qualitatively to half quantitatively, and the interpreting section can be drawn. The results show that the detection effect for the shaft quality is significant by elastic wave technique, and the delineation of abnormal areas is accurate. Its guidance function is better for pro- duction.

Computational Complex Method for Finite Elastic Plane Problem with Multiple Elliptical Holes

把多复变量应力函数和边界配点最小二乘法相结合，计算含有任意多个椭圆孔有限大小弹性板的应力场．每个孔的大小、位置为任意．板的边界由下列四种边界条件以及它们的组合所组成：１）已知Ｐｘ和Ｐｙ的应力边界，２）已知Ｖｘ和Ｖｙ的位移边界，３）已知法向位移ＶＮ和切向力ＰＴ的混合边界，４）已知法向力ＰＮ和切向位移ＶＴ的混合边界．编制了相应的ＦＯＲＴＲＡＮ程序，进行考题和算例分析，结果表明本方法行之有效．

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

FURTHER RESEARCH ON THE SPLINE MODEL METHOD OF KED ANALYSIS IN A PLANAR FLEXIBLE LINKAGE

This paper relates to the deep research on the Splinc Model Method of KED analysis. With the use of cubic B-splinc function as a link’s transverse deflection interpolation function, the principle of virtual displacement is presented as a basic theory for the general formulation of the equations of motion, and thus abandoned the kinematic assumption and the instantaneous structure assumption which arc used in the Spline Model Method. In thc same time, the nonlinear terms sue as coupling terms between thc rigid body motion and elastic deformation arc included. New member’s spline models are established. Mass matrix, Coriolis mass matrix, normal and tangential mass matrix, linear stiffness matrix, nonlinear stiffness matrix and rotation matrix arc derived. The kinematic differential equations of a member and system are deduced in the end. The Newmark direct integration method is used as the solution scheme of the kinematic differential equations to get the periodic response.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

Non-pneumatic mechanical elastic wheel natural dynamic characteristics and influencing factors

Non-pneumatic tire appears to have advantages over traditional pneumatic tire in terms of flat proof and maintenance free.A mechanical elastic wheel(MEW) with a non-pneumatic elastic outer ring which functions as air of pneumatic tire was presented.The structure of MEW was non-inflatable integrated configuration and the effect of hinges was accounted for only in tension. To establish finite element model of MEW, various nonlinear factors, such as geometrical nonlinearity, material nonlinearity and contact nonlinearity, were considered. Load characteristic test was conducted by tyre dynamic test-bed to obtain force-deflection curve. And the finite element model was validated through load characteristic test. Natural dynamic characteristics of the MEW and its influencing factors were investigated based on the finite element model. Simulation results show that the finite element model closely matched experimental wheel. The results also show that natural frequency is related to ground constraints, material properties, loads and torques. Influencing factors as above obviously affect the amplitude of mode of vibration, but have little effect on mode of vibration shape. The results can provide guidance for experiment research, structural optimization of MEW.

Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory

In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory.The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs.The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams.The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle,which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions.Based on the numerical experiments,it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

Test and Analysis of the Sound Insulation Performance of Four Types of Timber Structure Floors under Jumping Excitation

To improve the impact sound insulation performance of building floors and meet the objective requirements for living comfort of residents,in this article,three kinds of elastic cushion materials,Portuguese cork board,BGL insulation sound insulation foam board,and EPP polypropylene plastic foam board,are applied to the sound insulation of a light frame wood floor structure of the same bedroom and compared to the ordinary floor.This study uses the transfer function method and transient excitation method to measure the sound insulation,damping ratio,and elastic modulus of materials,as well as the sound insulation of the floor under the jumping excitation method of daily behavior.Through comparative analysis,the results and factors of improving the sound insulation performance of the floor are obtained,according to which three types of elastic cushion materials and the floor covering composed of them have higher vibration and noise reduction performance.Among them,the overall sound insulation performance of BGL board floor is the highest,followed by EPP board and cork board floor,and ordinary OSB floor is the lowest.Under the jumping excitation method,three floating floors can improve the impact sound insulation performance of the middle and low-frequency bands.

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Temperature field analysis and its application in hot continuous rolling of Inconel 718 superalloy

A coupled thermo-mechanical model containing metal flow and temperature field for calculating temperature variation has been developed on fourteen-pass hot continuous rolling of round rod for Inconel 718 alloy using 3D elastic-plastic finite element method （FEM）. The temperature of characteristic analysis points in the intermediate cross-section of the workpiece has been simulated at initial temperature ranging from 960 to 1000 ℃ and initial velocity in range of 0.15-0.55 m·s^-1. Based on finite element analysis and microstructural observation in cylindrical hot compression experiments, the appropriate hot continuous rolling technologies have been designed for rod products with different diameters. For a real rolling practice, the simulated surface temperature was examined and is in good agreement with the measured one.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

Application of the extended Fourier amplitude sensitivity testing(FAST)method to inflated,axial stretched,and residually stressed cylinders

This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE Ⅱ PLANE STRESS CRACK

The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theoryhave been completely. dbandoned and the correct .formulations of matching conditionsat the elastic-plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopted) will the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary. near the crack line, the plastic .stresses, the length of the plastic zone and theunit normal vector of the elaslic-plastic boundary. which sufficiently precise nearthe crack line region, hare been given.