The finite-element method has been used extensively for elastic problems. The method is a powerful one and is reserved for problems that can be programmed and solved by computer techniques. The literature over the last 20 years abounds with references to finite-element development and application,and many all-purpose finite-element codes are now commercially available. As the name implies,the basic building block is an element of finite dimensions . The object to be analyzed is divided into a number of these small elements. These elements are joined at corners ,and it is usually assumed that the stress is uniform throughout the element. The element distortions are computed by conventional theory. The total behavior of the structure depends on the intergrated effects of each of the parts. Thus since a part is usually divided into a multitude of element,a solution is possible with the help of a computer. The accuracy of the finite-element method depends on both the type of problem and the number and type of elements selected. In the late 1960s the success of the finite-element problems stimulated the work of extending the application of the method to the area of plastic deformation. It was originally applied to elastic-plastic problems,ones in which the plastic strain is of the order of the elastic one. Here the strain is separated into an elastic part and a plastic part. The elastic part is governed by Hooke’s law, while the plastic part used the Prandtl-Reuss equations. The nonlinearity in the constitutive equations is satisfied iteratively. This can be accomplished by either the initial-strain method or the initial-stress method. Of these to methods, the initial-stress method has found increased favor. With this method,the deformation zone can be very accurately determined.It needs to be pointed out that the finite-element method is not geometry-dependent. Rather,with this technique one can analyze arbitrary geometrically complicated structures. For large deformations it is generally not necessary to consider elastic deformations. In fact ,in the analysis of most metal forming operations, as a rule one can neglect them and employ the rigid-plastic material model. An exception to this rule is that it is generally mandatory to utilize elastic-plastic analysis in order to be able to predict foaming defects. Defects comprise the initation and growth of internal or surface cracks in the deforming metal or the localization of deformation through plastic instability, which could impair the dimensional accuracy of the finished workpiece. Similarly, residual stresses in the unloaded workpiece cannot be evaluated using a rigid-plastic model.
在有限元方法已被广泛用于各类弹性力学问题。这个方法是一种强有力的和被保留给问题,可编程计算机技术,解决了。文学在过去的20年里布满了引用有限元技术的发展与应用,许多通用有限元代码现在投放市场。 顾名思义,这个基本积木是一个元素的有限尺寸。这个对象来进行分析分成许多这些小的元素。这些元素在角落,并加入通常假定的应力是统一的元素。元素是可以通过传统的理论。总性能的综合效应结构取决于每个人的部分。因此,既然部分通常可分为多种元素,是可能的解决方案的计算机。有限元方法的精度取决于这个类型的问题和数目和类型的元素。 在20世纪60年代后期的成功刺激的工作问题的有限元方法的应用延伸的塑性变形。它最初是用于弹塑性问题,还是在塑性应变为弹性。这里的应变分割成一个有弹性的部分和塑料部件。弹性部分是由虎克定律,塑料部件使用Prandtl-Reuss方程。非线性本构方程是满意的。这可以通过或initial-strain法或者initial-stress方法。这些方法,initial-stress方法发现增加有利。用这种方法,变形区可以非常准确地确定。 需要指出的是,采用有限元方法是不geometry-dependent。相反,用这种技术可以分析任意几何构造复杂。 对于大变形一般不需要考虑弹性变形。事实上,在分析成形操作,大多数人会忽视了他们的规则和雇佣刚塑性材料模型。一个例外是,它通常是强制性的利用弹塑性分析为了能够预测泡沫缺陷。组成的邀请和增长的缺陷的内部和表面裂缝的本土化的变形金属或塑料失稳变形通过,否则会损害的尺寸精度的工件。同样,残余应力在卸工件不能用一个刚塑性模型。
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