Statics,dynamics, and stability of composite panels with gently curved orthotropic layers. 1. Statics and vibrations

Two approaches to the investigation of the stress-strain state and of free vibration frequencies of laminate panels with gently curved orthotropic layers are elaborated. The first approach is based on the analytical separation of variables, and in the second one the variables are approximated with respect to the transverse coordinate by the polynomials obtained from the Ambartsumyan iteration approach. Since the unknown functions in this approximation are related to the front surfaces of the structure, the panel can be divided, if necessary, into separate strips across the thickness with a rigid or sliding contact between them. The displacements on the lower surface can be excluded.Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 423–434, 1999.     

变形浅水波方程组的一个非线性变换及其应用

本文用齐次平衡方法导出了变形浅水波方程组的一个非线性变换,借助该变换得到了方程组的精确孤立波解。     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

Snap-buckling of dished shallow shells under line loads

I.IntroductionDishedshallowshellsareakindofthinshellswhichconsistofashallowconicalshellwithacircularplateatthecenterregion.Intheself~controlsystemofprecisioninstrumellts,thesnap-bucklingphenomenonofdishedshallowshellsisusuallyusedasacontrolinformation.Becauseofthedifficultiesinthenon-linearanalysis,thesnap-bucklingproblemofdishedshallowshellshasneverbeenattempted.Atpresent,thedesignforthesnap-bucklingofdishedshallowshellshasbeendonemainlybasedonexperienceandexperimentsl'],butlackenoughtheoret…     

开孔浅球壳的非线性动力响应及其动力稳定

本文建立了具轴对称变形、考虑横向剪切影响的浅球壳的非线性运动方程:对周边弹性支承开孔浅球壳的非线性静、动力响应及动力稳定问题进行了探讨.在解题方法上,对位移函数在空间上采用正交配点法离散.在时间上采用平均加速度法(Newmark-β法)离散.变求解一组非线性微分方程为求解一组线性代数方程.文中给出了不同情况下的若干数值结果,且与有关文献的结果作了比较.     

Snap-buckling of dished shallow shells under uniform loads

I.Intr0ducti0nDishedshallowshellsareakindofthinshellswhichconsistofashallowconicalshellwithacircuiarplateatthecenterregi0n.Thesnap-bucklingphenomenonofdishedshallowshellsisusedasacontrolinformationofthepress-temperatureselfcontroIsysteminprecisioninstrume…     

相邻多个浅圆弧凹陷地形对平面SH波散射的级数解

本文采用解析法研究相邻多个线圆弧凹陷地形对平面SH波散射问题。文中由分离变量法把相邻多个圆弧凹陷对平面SH波的多重散射表示为各局部坐标中的级数之和,再利用Graf加法公式的内域和外域表达式进一步表示某个局部坐标中的双重无穷级数形式。问题最后可归结为求解一组无穷型的线性代数方程。文末给出了相邻两个等直径浅圆弧凹陷地形的多种深宽比对地面运动的影响的计算结果,并讨论了浅圆凹陷地形对波的屏蔽及它们之间的相互作用。     

SINGLE-LAYER FINITE ELEMENT APPROXIMATION OF 3D NAVIER–STOKES EQUATIONS WITH FREE BOUNDARIES FOR SHALLOW WATER FLOWS

In order to simulate flows in the shallow water limit, the full incompressible Navier–Stokes equations with free boundaries are solved using a single layer of finite elements. This implies a polynomial approximation of the velocity profile in the vertical direction, which in turn distorts the wave speed. This fact is verified by numerical results: the wave speed depends on the vertical discretization. When at least two layers of finite elements are used, the boundary layer at the bottom can be simulated and the correct solution for the shallow water limit is recovered. Then this algorithm is applied to the prediction of Tsunami event.     

A DEPTH-INTEGRATED 2D COASTAL AND ESTUARINE MODEL WITH CONFORMAL BOUNDARY-FITTED MESH GENERATION

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications.     

LIQUID-SOLID COUPLED SYSTEM OF MICROPUMP

This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to characterize the flows in micropump. The finite element method is used to obtain a matrix equation of fluid pressure. The fluid pressure equation is combined with the vibration equation of a silicon diaphragm to construct a liquid-solid coupled equation for reflecting the interaction between solid diaphragm and fluid motion in a micropump. Numerical results of a mode analysis of the coupled system indicate that the natural frequencies of the coupled system are much lower than those of the non-coupled system. The influence of additional mass and viscous damp of fluid on the natural frequencies of the coupled system is more significant as the pump thickness is small. It is found that the vibration shape functions of silicon diaphragm of the coupled system are almost the same as those of the non-coupled system. This paper also gives the first-order amplitude-frequency relationship of the silicon diaphragm, which is necessary for the flow-rate-frequency analysis of a micropump.