几何相似体应力-应变分布相同时的载荷关系

The Load Relationships of the Geometric Similar Components under the Same Stress-strain States

为了保证几何相似模型与原件具有完全相同的应力-应变分布,必须对几何相似模型施加与实际构件成对应比例的各种载荷,因此需要寻求几何相似模型在应力-应变分布完全相同时各种外加载荷的比例关系。从相似理论入手,以2端固支的矩形梁下表面边线中点的应力解析表达式为基础进行推导,得出相应的理论载荷关系,并用算例在弹塑性状态下验证了所得关系的正确性。得到的结论是:对于2个几何相似构件,若几何相似系数为kl,则当外加集中载荷的载荷系数为k2l、均布线载荷的载荷系数为kl、均布面载荷的载荷系数为1时,2构件的应力-应变分布完全相同。

Normally,the original components are lessened or enlarged proportionally to build the geometric similar models when large scale components are tested or studied by means of finite element analysis（FEA）.In order to ensure that the same stress-strain states present between the considered model and the original component,the loads corresponding to the original components in proportion should be applied to the geometric similar models.Therefore,it is important to study the load relationships among these geometric similar components with the same stress-strain states.Based on the stress expressions of middle point on the below edge of immobile rectangular cross section beam,the loads＇ theoretical relationships are obtained using the similarity theory.The correctness of these relationships is verified by the components under elastic and/or plastic stress-strain states.The conclusions are shown as follows： for the two components with geometric similar coefficient kl,if the concentrated force coefficient is k2l,the uniformly distributed line force coefficient is kl,or the uniformly distributed plane force coefficient is 1,then the two components are completely the same in stress-strain state.