Simplified numerical modeling and simulation of compositelaminated plates by the variational asymptotic method

This paper develops a simplified model for composite laminated plates by the variational asymptotic method (VAM) in order to efficiently analyze the nonlinear, one-way couples problem. It deduced the 3D energy expressions based on the decomposition of rotation tensor (DRT). The 3D laminated plate model is decomposed into a 2D plate analysis and a non-linear 1D analysis along the normal direction. The approximate energy after dimensionality reduction was deduced and converted to a form of reissner model. The 3D field recovery relations are provided to obtain accurate stress distribution through the thickness direction. The cylindrical bending example of 4-layer composite plate shows that the 3D stress fields recovered by this theory have better accuracy than those by the classic laminated theory (CLT), which indicates the validity of this model.     

Numerical Prediction of Frequency of Delaminated Advanced Grid Stiffened plate

The paper aims to investigate natural frequency of delaminated advanced grid stiffened composite plates by hump resonance method.The composite laminated plate element and the rib element are adapted to simulate the laminated plate and the ribs.Based on the composite laminated plate and beam element model considering first-order shear effect,a damping model on the basis of Rayleigh damping model in conjunction with Adams' strain energy method(MSE) and a Hertz nonlinear dynamic contact model to avoid the overlap and penetration phenomenon between the upper and lower sub-laminates at the delaminated region.A numerical analysis method of dynamic response for the delaminated composite plates is carried out by precise time-integration method,and then the natural frequencies are achieved when the dynamic deflections reach the hump peak.For the frequency-domain analysis provided in the former research papers,it is a difficult problem to avoid the embedded phenomenon in the mode shapes at the delamination zone,while in the current time-domain analysis,the embedded phenomenon can be successfully overcome by using nonlinear contact model.By vibration excitation test,the specimens were excited by different excited frequency and the amplitude frequency response characteristics obtained are used to extract the frequency.The extracted frequencies of the narrow delaminated composite plates measured,which agrees well with the predicted natural frequencies.     

ANALYSIS OF NONLINEAR PROBLEMS OF LAMINATED PLATES BY USE OF PERTURBATION AND WEIGHTEDRESIDUAL METHOD

This paper solves the geometrically nonlinear problems of symmetric, cross-ply laminated anisotropic rectangular plates subjected to uniformly distributed load by the higher-order shear deformation theory and taking an advantage of the perturbation and the weightedresidual method. First, with the help of the perturbation, the nonlinear partial equations have been changed into linear ones. This paper can solve these linear ones by the weighted-residual method. The combination of quintic B-spline functions are chosen as the basis of trial function and Dirac delta functtion, the weighted function. The method used in this paper is simple, direct and efficient. The numerical results show a good convergence and they are in good agreement with the available data.     

Out-of-Plane Mechanical Properties of Masonry Wall with Homogenization

Based on the three-dimensional homogenization theory, the Characteristic 3D elementary pattern in the masonry was established. The homogenized masonry wall was considered as a vertical plate with four supports. The plate theory was used to research the out-of-plane mechanical properties of masonry panels. Homogenization models with theory of thin plates and theory of medium and heavy plates were given and the calculation formula of deflection of homogenization masonry wall were deduced as well. The mid span deflections of 120 mm, 180 mm, 240 mm and 370 mm masonry walls with both fixed and variable ratio of height to width were analyzed. The applicability of two kinds of plate theories on homogenization masonry walls of different sizes was obtained. This methodology was practical and the masonry theory was improved.     

A Simplified Thermoelastic Model for Composite Iaminated Shells

To effectively analyze the one way coupled thermoelastic problem for composite laminated shells, a simplified thermoelastic shell model based on the variational asymptotic method (VAM) was developed. The 3 D energy functional for composite laminated shell was established according to the Hamilton extended principle. Then the 3 D energy was asymptotic expanded into a series of 2 D approximation energies by taking advantage of the inherent small parameters. Finally, the approximate energy was converted to the form of Reissner Mindlin model, and the 3 D recovery relationships were deduced to accurately predict the 3 D field distribution along the thickness direction. The cylindrical bending example of a four layer composite laminated shells under the sinusoidal surface load and temperature field shows that the modeling speed is fast (equivalent single layer model, which can reduce two or three order calculations compared to the 3 D finite element method), and the nonlinear approximation ability is excellent (convergent to the exact solution).     

Indentation Cracking Mechanical Analysis of ZrO2 Laminated Ceramics

The formation of indentation cracking has some relationship with the transformation stress induced by martensitic transformation, besides the relationship with the residual stress by volume change in the plastic zone in ZrO_2 laminated ceramics. Whereas surface residual compressive stress controls the expansion of surface cracks. Contributions of the transformation driving force and surface compressive stress are not considered in the traditional indentation theory. Therefore, fracture toughness value measured by the traditional method is usually lower than the practical one in ZrO_2 laminated ceramics. When indentation-fracture method is used, the value is more reliable.     

Singularly Perturbation of the Nonlinear Three Species Prey-predator Reaction Diffusion System

A class of nonlinear three species in the biomathematics is considered with the prey-predator singularly perturbed problems for the reaction diffusion system method of differential inequalities. Under suitable conditions, the existence and asymptotic behavior of solution for the initial boundary value problems are studied with the theory of differential inequalities. The theory of differential inequalities is really to constructing two auxiliary functions, which are super and lower solutions of the system respectively. And then the super and lower solutions are satisfied corresponding inequalities. Finally, there is a solution of the system between the super solution and lower solution. Then the existence of the solution for the system is proved and the asymptotic estimation is obtained.     

Nonlinear Finite Element Analysis of Reinforced Concrete Transferring Joints with Inclined Columns

A nonlinear finite element analysis using ANSYS is applied to the vertical mechanical behaviors of three specimens of reinforced concrete transferring joints with inchned columns, which are used in high - rise buildings. A comparison is made between the analytical achievements and the test results, including the mechanical behaviors, load - transferring path and the failure modes, and a good agreement is obtained. The reliability of the software ANSYS in the nonlinear analysis of such reinforced concrete structures is verified and developed.     

Analysis on the stability of traffic flow with the information of two preceding cars

The stability analysis is one of the important problems in the traffic flow theory, where the congestion phenomena can be regarded as the instability and the phase transition of a dynamical system. An extended optimal velocity model is deduced by considering the effect of the information of two leader cars. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point by applying the nonlinear analysis. The numerical simulation results demonstrate the analytical results and show that the traffic congests are suppressed more efficiently by considering two vehicles ahead. Therefore, the next-nearest-neighbor car has strong effects on traffic dynamics and plays an important role on stabilizing the traffic flow.     

Vibration characteristics of face-gear transmission system with parametric excitation

In order to study the influences of different factors on nonlinear dynamics of face-gear transmission system, a nonlinear dynamic model is presented. This model includes backlash, general transmission error, time-varying meshing stiffness, meshing damping, bearings and external load, etc. Based on numerical analysis theory of nonlinear dynamics, the equations are solved and the bifurcation characteristics with different parameters are obtained. And the calculation results show that increasing the backlash and time-varying meshing stiffness will augment the dynamic load of system, but increasing the mesh damping will reduce the dynamic load effectively.     

VISAR Data Reducing Method and Its Application to Impact Experiment

Identification and adjustment on the disfigurements of original data of VISAR are probed by developing software for VISAR data reducing based on measure theory. Then the software is applied to plate impact experiment of ceramics. The disfigurements of light intensity data are identified and adjusted through Lissajou~ figures. The results indicate that VISAR data are reduced quickly and effectively by the software, and the exact free surface velocity history is obtained.     

Axisymmetric Loaded Elastic Circular Plate on Multi Layered Soil

An analytical solution of the elastic circular plate on multi layered soil can be obtained by using the transfer matrix solutions for displacements and stresses of multi layered soil. This solution is based on the continuity of vertical displacements and the smooth contact conditions between a multi layered soil surface and the elastic circular plate. Numerical calculation and analysis are carried out by the computer program compiled for this purpose. The numerical results show that the rigidity of the elastic circular plate greatly influences the displacement of the circular plate and the normal stresses under the center of the circular plate.     

NONLINEAR COUPLING IN THERMOELAST1C THEORY AND A SOLUTION TO THE PROBLEM IN THE HALF SPACE

It's recommended that the term coupled in temperature and strain is nonlinear and is significant in thermoelastic theory. Using the solution of linear coupled and uncoupled theory and selecting appropriate general coordinates, authers approach the nonlinear coupled problems with a variational method. A solution to the problem in half space, is given. It is shown that the difference between the nonlinear coupled theory and the linear coupled or uncoupled theory would be notable when the amplitute of temperature is much larger than that of the reference slate.     

Research on Bifurcation and Chaos Characteristics of Meso-Scopic Fracture Process of Rock

On the basis of test results of meso-scopic fracture process and evolution of microcracks of rock in uniaxial compression,the number and orientation of microcracks at each stress level are obtained.A mathematical model for describing the germination and evolution of microcracks is proposed.The bifurcation and chaos behaviours of the evolution of microcracks and meso-scopic fracture process are studied for the first time with the bifurcation and chaos theory of modern nonlinear science.When the characteristic values which represent the gernimation and closure effect of microcracks take certain values,the evolution of microcracks can be described by the Logistic equation.Therefore,the evolution of microcracks of rock has the bifurcation and chaos characteristics.[WT5HZ]     

Finite element model of coupled systems for vibration reduction plates with smart constrained layer damping

Considering the relationships of coupling movement and compatible displacement among bonding layer, piezoelectric layer, damping layer, and base structure, a finite element dynamic model of coupled systems for vibration reduction plates is established. The model combined with piezoelectric theory, finite element theory and ADF model of viscoelastic damping material can be suitable for vibration model of complex SCLD structure. The dynamics parameters for clamped-clamped steel plate with partially treated smart constrained layer damping are obtained by theoretical calculation, ANSYS modal analysis and modal experiment. The results show that theoretical values are closer to the test results and ANSYS analysis, and the methods proposed is more accurate and effective.     

A Method for Solving Strong Nonlinear Vibration

A method,stroboscopic harmonicbalance method which is used to solve strong nonlinear system, is proposed. The method is used to find the solution of strong nonlinear system. In investigation,the existence conditions of primary resonance solution and subharmonic resonance solutions are obtained. The results which are obtained by the stroboscopic harmonicbalance method are compared with those by computer numerical simulation. The results show that the stroboscopic harmonicbalance method is correct in qualitative analysis and it can meet the demands in engineering.     

Analysis of the Mechanical Behavior of Gusset Plate to CHS KK joints

A nonlinear finite elements analysis was carried out to investigate the failure modes and the ultimate strength of gusset plate to CHS KK joints. The effects of web loading proportion, geometric parameters and axial stress in chord on the ultimate strength were considered. It was found that the ultimate strength of gusset plate to CHS KK joints was greatly decreased with the increase of web loading proportion when the proportion value was positive; however, the web loading proportion had less effect on the ultimate strength when the proportion value was negative. And with the varying of web loading proportion, the effect of the axial stress in chord on the ultimate strength of KK joints had a complex effect on the joint mechanic behavior. Based on the regression analysis, a formula was proposed for predicting the ultimate strength of gusset plate to CHS KK joints.     

Study and Application of High Precision Nonlinear Plane Stress Element

A tangent stiffness matrix for quadrilateral plane stress element under large rotation with small strain is proposed in this paper,The corresponding program based on this theory has been worked out;The computation of examples with analytic values has verified that the element's formulation, its program given in this paper have strong nonlinear computation ability;A nonlinear whole-course analysis of stone arch bridge has been done in this paper.The computations presented preferably a comprehensive understanding of nonlinear characteristics of stone arch bridge with small span and could be beneficial for the engineer designers.     

LARGE DEFLECTION OF A CIRCULAR PLATE ON PASTERNAK FOUNDATION UNDER A CONCENTRATED LOAD AT THE CENTER

Based on Karman's nonlinear foundamental differential equations, the new method combines perturbation method with integral equation method is forward to solve nonlinear bending of a clamped circular plate on Pasternak foundation under a concentrated load at the center. This method is simple and easy to use. The numerical results show that the present solution is reliable.