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A novel formulation of material nonlinear analysis in structural mechanics
Defence Technology ( IF 5.1 ) Pub Date : 2020-06-30 , DOI: 10.1016/j.dt.2020.06.018
Himanshu Gaur , Anupam Srivastav

This article demonstrates a novel approach for material nonlinear analysis. This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior. Use of elastic moduli is eliminated. Instead, stress and strain functions are used as the material input in the analysis procedure. These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting. This way, the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior. It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results, easy to adopt and simple in calculations. The method eliminates all types of linearity assumptions in basic derivations of equations and hence, eliminates all types of possibility of errors in the analysis procedure as well. As it is required to know stress distribution in the structural body by proper modelling and structural idealization, the proposed analysis approach can be regarded as stress-based analysis procedure. Basic problems such as uniaxial problem, beam bending, and torsion problems are solved. It is found that approach is very suitable for solving the problems of fracture mechanics. Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated. The approach solves the fracture problem with relative ease in strength of material style calculations. For all problems, results are compared with the classical displacement-based liner theory.



中文翻译:

结构力学中材料非线性分析的新公式

本文演示了一种用于材料非线性分析的新颖方法。该分析过程消除了繁琐而冗长的逐步增量过程,然后消除了经典采用的迭代过程,并在材料行为的线性和非线性范围内给出了直接结果。消除了弹性模量的使用。相反,应力和应变函数用作分析过程中的材料输入。这些应力和应变函数是通过曲线拟合的方法直接从材料的应力-应变行为得出的。这样,在分析中利用了整个应力-应变图,当载荷处于材料行为的非线性范围内时,自然地揭示了结构的响应。发现这是迄今为止材料非线性分析所采用的一种出色的计算程序,其给出的结果非常准确,易于采用且计算简单。该方法消除了方程式基本推导中的所有类型的线性假设,因此也消除了分析过程中所有类型的错误可能性。由于需要通过适当的建模和结构理想化来了解结构体内的应力分布,因此所提出的分析方法可以视为基于应力的分析程序。解决了诸如单轴问题,梁弯曲和扭转问题之类的基本问题。发现该方法非常适合解决断裂力学问题。还评估了具有中心裂纹和双悬臂梁试样的板的能量释放率。该方法可以相对轻松地解决材料样式计算强度方面的断裂问题。对于所有问题,将结果与基于经典位移的线性理论进行比较。

更新日期:2020-06-30
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