一道例题的探索

题目如图1,已知OPQ是半径为1,圆心角为π/3的扇形,C是扇形弧上的动点,ABCD是扇形的内接矩形,     

关于定积分近似计算中矩形法的误差估计

利用拉格朗日中值定理给出复合矩形法的误差估计,并指出复合矩形法只有在等分的次数很大的时候才能比较精确的估计所求定积分的值.最后,给出复合矩形法、复合梯形法及复合抛物线法的误差估计实例.     

一个新的非常规各向异性元的收敛性分析

构造了一个新的非常规各向异性Hermite型矩形单元并据此对二阶椭圆问题提出了一个混合元格式,同时给出了该格式的收敛性分析.     

源于课本 高于课本——一道数学应用题赏析

纵观近几年来的江苏省高考数学试题和各地的模拟试题,源于课本的题型占据了一定的份量,如这次扬州二模试题(这次考试为扬州、泰州、南通联考)的第18题就是一个很好的例子,本试题为应用题,试题新颖,牵涉到函数,导数,不等式的     

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.     

THREE-DIMENSIONAL THERMOELASTIC ANALYSIS OF FUNCTIONALLY GRADED PLATE

Three-dimensional thermoelastic analysis is presented for an orthotropic functionally graded rectangular plate,which is simply supported and isothermal on its four lateral edges.With the assumption that material properties have arbitrary dependence on the thickness-coordinate,a Peano-Baker series solution is obtained for the thermoelastic fields of the functionally graded plate subjected to mechanical and thermal loads on its upper and lower surfaces by means of state space method.The correctness of the obtained series solution is validated through numerical examples.The influence of different material properties distributions on the structural response of the plate is also studied.     

含诱导缺陷薄壁圆管耐撞性优化设计

运用移动最小二乘曲面拟合技术和遗传算法优化技术,建立一套完整的结构耐撞性优化设计技 术。设计了一个具有高效吸能能力的薄壁圆管结构含诱导缺陷薄壁圆管结构,给出了含缺陷薄壁圆管结 构耐撞性优化设计结果。结果显示,设计的薄壁圆管结构具有好的吸能效果,该结构设计简单,便于在结构设 计中使用。     

LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT METHODS FOR DARCY-STOKES PROBLEMS

In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson＇s equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.     

二维矩形件排样的切割式填充算法

针对二维矩形件排样困难的问题,提出了一种简单且高效的切割式填充矩形件排样算法.首先根据对矩形件进行优化排样的要求,建立起数学规划模型.然后采用降维的思想,对矩形行列虚拟化分割.在第一行(列)上进行矩形件排样,使其填充率最高.接着将此行(列)切割掉,形成新的矩形.最后重复上述步骤,直到矩形无法再填充下任何一种规格的矩形件为止.数值实验表明了切割式填充算法的可行性和高效性.     

巧解高考题

题目（2008年江苏）某地有三家工厂。分别位于矩形ABCD的顶点A，B及CD的中点P处，已知AB=20km，CB=10km，为了处理三家工厂的污水，现要在矩形ABCD的区域上（含边界）。且与A，B等距离的一点O处建造一个污水处理厂，