基于最小二乘法的Lagrange分析方法研究  

Lagrangian analysis method based on least square

作　　者：陶为俊[1] 浣石[1] 蒋国平[1] 

机构地区：[1]广州大学工程抗震中心,广州510405

出　　处：《振动与冲击》2012年第21期98-101,142,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金(10972060)

摘　　要：Lagrange分析方法是通过测量各个拉格朗日位置处的物理量历程来分析材料内部该位置处的其他物理量的变化,进而认识材料的动态力学性能。但现有的Lagrange分析方法在已知应变情况下,求解方法仍有不足。针对这一情况,将反解法和自洽检验法相结合,提出了基于最小二乘法的Lagrange反解法。该方法的理论精度能够实现沿径线的M阶导数Mσ/hM≡0(M为迹线数),并且该方法满足自洽检验法,算法本身不会造成数据处理结果的失真,其精度完全取决于试验精度和数据量。利用该方法对一组混凝土在冲击作用下的实验数据进行了处理,计算得到了相应的粒子速度波形、应力波形以及加、卸载全过程的应力-应变曲线,从而揭示出混凝土材料与应变率相关的弹-塑性本构关系的特征。Lagrangian analysis method is a method with which the physical variables of each Lagrangian positions are measured to analyze the other physical variables of a material, and then the dynamic mechanical properties of the material can be determined. However, the existing Lagragian analysis method is still inadequate with the strain of a material known. Here, a new Lagrangian analysis method with least square combining the inverse method and self-consistency examination was proposed. The theoretical accuracy of the method could achieve M-order partial derivatives a^m σ/ah^M=0 along the particle line （M is the number of particle lines）. And the method satisified the self-consistency examination, the algorithm itself did not cause the distortion of the data processing results, its accuracy depended entirely on the test accuracy and the amount of test data. Test data for a set of concrete under action of impact were processed with the method, the corresponding particle velocity wave, stress wave, and stress - strain curves of the whole process of loading and unloading were calculated, and it was revealed that the elastic - plastic constitutive characteristics of the concrete is related to its strain rate.

关 键 词：Lagrange分析 本构关系 应力-应变 最小二乘法 混凝土 

分 类 号：O347.3[理学—固体力学] V216.55[理学—力学]