结构冲击畸变问题的直接相似方法研究
A DIRECT SCALING METHOD FOR THE DISTORTION PROBLEMS OF STRUCTURAL IMPACT
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摘要:结构受冲击时由不同材料引起比例模型与全尺寸原型的畸变, 通常通过修正比例模型的速度或密度进行补偿. 然而传统的修正方法, 存在需预先测试结构响应、依赖特殊本构方程、不能反映动态过程的缺陷, 因而限制了相似理论在比例模型试验中的直接应用. 本文提出了一种不同材料畸变问题的直接相似方法. 它通过建立应变率区间上比例模型预测的流动屈服应力与原型流动屈服应力的最佳逼近关系, 直接获得了修正速度或修正密度的比例因子, 完成了比例模型与原型的动态相似关系. 基于Norton-Hoff, Cowper-Symonds, Johnson-Cook三种经典的本构模型, 研究了材料应变率敏感性特征参数、参考应变率、屈服应力、密度在动态相似关系中的作用. 并通过受质量冲击的折板结构算例, 验证了直接相似方法的有效性. 分析表明, 本文提出的直接相似方法不需要预先测试结构的响应, 不依赖特殊的本构方程、强调动态相似特性, 具有直接、高效、通用的特点. 此外, 动态相似关系的最佳逼近效果, 受材料应变率敏感性特征参数控制, 屈服应力、密度和参考应变率影响不大; 当比例模型应变率敏感性特征参数与原型相近, 可获得最佳逼近.Abstract:The distortion of structural impact arising from the use of different materials between the full-size protype and the small-size scaled model is usually compensated by the correction for the velocity or density of the scaled model. However, the traditional correction methods are limited for the application of similarity laws because of some inherent defects such as the needs to test structural response in advance, the dependence for the special constitutive equation and the inability to reflect dynamic process of impact. In the present paper, a direct scaling method for distortion problems is proposed. Based on the best approximation relationships between the predicted flow yield stress of the scaled model and the flow yield stress of the prototype on strain rate interval, the scaling factor for the corrected velocity or the corrected density are obtained directly, and the dynamic similarity relations between the scaled model and the prototype are established. Based on the Norton-Hoff, Cowper-Symonds and Johnson-Cook constitutive models, the influences of material parameters of the strain-rate-sensitive, the reference strain-rate, the yield stress and the density for the dynamic similarity relations are studied. And a crooked plate under impact mass is used to verify the effectiveness of the proposed directly scaling method. The analysis shows that the proposed directly scaling method does not need to test the structural response information in advance, does not depend on the specific form of constitutive equation and emphasis the dynamic similarity characteristics, so that it has the direct, efficient and universal characteristics. The optimal approximation effects of the dynamic similarity relations are mainly controlled by the material strain-rate-sensitive characteristic parameters, while the reference strain-rate, the yield stress and the density have little influence. When the material strain-rate-sensitive characteristic parameters of the scale model are similar to those of the prototype, the best dynamic approximation effects can be obtained.