h和p方法区别.doc
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1、(word完整版)h和p方法区别Summary: In terms of computing time, the h and p methods will have about the same requirements。 In each case you are solving for about the same number of nodes. The hmethod increases the number of nodes by adding more elements. The p-method increases the number of nodes by increasing
2、 the order of the shape function。 h-method采用简单的形状函数,要增加节点通过增加单元数量而各个单元形状函数不变p-method采用比较复杂单元形状函数,要增加节点通过增加单元阶数,而数量不变。hmethod适用于任何类型分析,但是p-method只适用于线性结构静力分析,根据所要解决的问题,hmethod需要的网格比p-method更细。p-method用较粗糙的网格也能达到较高的精度。Overview: There are two common methods of solving problems within finite element pro
3、grams. These methods are the h-method and the pmethod。 With each method the geometry to be analyzed is broken into finite elements. The difference between the two methods lies in how these elements are treated. The hmethod uses many simple elements, whereas the pmethod uses few complex elements。 HMe
4、thod: The simplest type of element has a linear shape function。 This means that the function for displacement across the element is linear. With the hmethod, the shape function of the element will usually be linear。 In an actual part, it is quite uncommon for the displacement to vary linearly。 The h
5、-method accounts for this by increasing the number of elements。 More accurate information is obtained by increasing the number of elements. The name for the hmethod is borrowed from mathematics. The finite element method was originally developed by the work of mathematicians, particularly those who
6、worked in the area of numeric integration。 The variable h is used to specify the step size in numeric integration. This variable name carried over into finite element analysis。 The upside to only using linear shape functions is that it easy to solve the element equations. The downside is that the st
7、rain across the element must be constant。 Strain is defined as the change in displacement divided by the original length. Since the displacement function is linear, strain must be constant throughout the element. Stress is derived from strain by using the modulus of elasticity, which is a constant.
8、Therefore, stress in an element with a linear shape function must be constant.Suppose that the actual stress across a part varied by the function represented by the curve in Figure 1。 If the problem was analyzed using linear shape functions, then the results for a course mesh would be represented by
9、 the bars in Figure 1.Figure 1: HMethod with Course Mesh If a part is modeled with a very course mesh, then the stress distribution across the part will be very inaccurate. In order to more accurately find the stress distribution across the part, we will need to increase the number of elements. If t
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