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首页> 外文期刊>Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods >A Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic–plastic and elastic–viscoplastic beams
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A Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic–plastic and elastic–viscoplastic beams

机译：Cosserat点元素（CPE），用于弹塑性和弹性粘塑性梁瞬态大平面运动的数值解

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The objective of this paper is to develop constitutive equations of a Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic– plastic and elastic–viscoplastic beams with rigid crosssections. Specifically, attention is limited to response of a material with constant yield strength. A yield function is proposed which couples the inelastic responses of tension and shear. Another yield function is proposed for bending which depends on a hardening variable that models motion of the elastic–plastic boundary in the beam’s cross-section. Evolution equations are proposed for elastic strains and the hardening variable and an overstress-type formulation is used for elastic–viscoplastic response. In contrast, with standard finite element approaches the CPE model needs no integration through the element region. Also, an implicit scheme is developed to integrate the evolution equations without iteration. Examples of transient large motions of beams, which are impulsively loaded, indicate that the CPE produces reasonably accurate response relative results in the literature and full three-dimensional calculations using ABAQUS.
机译：本文的目的是开发一个Cosserat点元素（CPE）的本构方程，用于求解具有刚性横截面的弹塑性和弹粘塑性梁的瞬时大平面运动的数值解。具体而言，注意力仅限于具有恒定屈服强度的材料的响应。提出了一个屈服函数，该函数耦合了拉伸和剪切的非弹性响应。提出了另一种弯曲屈服函数，该函数取决于硬化变量，该变量模拟梁横截面中弹塑性边界的运动。提出了用于弹性应变和硬化变量的演化方程，并为弹性-粘塑性响应使用了过应力型公式。相反，使用标准的有限元方法，CPE模型不需要在整个元素区域进行积分。而且，开发了一种隐式方案来集成演化方程而无需迭代。脉冲加载的梁的瞬时大运动示例表明，CPE在文献和使用ABAQUS的完整三维计算中产生了相当准确的响应相对结果。

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