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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models
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A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models

机译：具有到任意三维材料模型的接口的混合混合有限元单元

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摘要

A theory for spatial beams and an associated mixed finite element formulation are presented. The basic kinematic assumption allows for finite rotations and transverse shear strains. The relation of the Green-Lagrangean strains to the beam strains is derived. A three-field variational formulation with independent displacements, rotations, stress resultants and beam strains is developed using the kinematic and static field equations and the constitutive equations. Higher order stress resultants are set to zero within the Euler-Lagrange equations. The formulation in this paper is restricted to rectangular cross sections. The interpolation of the beam strains consists of two parts. The first part is identical to the stress resultant interpolation. The second part describes cross section warping and allows for transverse normal strains. Within this approach an interface to arbitrary three-dimensional constitutive laws can easily be realized. Due to the mixed interpolation technique full Gauss integration in length direction of the beam element can be applied to obtain a locking free element formulation. The effectiveness of the method is demonstrated by means of several numerical examples. We present results for elasticity, inelasticity, and stability problems and evaluate the load carrying capacities of spatial beam structures. The essential feature of the new element is the robustness in nonlinear applications. It allows very large load steps in comparison to other element formulations.
机译：提出了空间梁的理论以及相关的混合有限元公式。基本的运动学假设允许有限的旋转和横向剪切应变。推导了Green-Lagrangean应变与束应变的关系。利用运动场和静态场方程和本构方程，开发了具有独立位移，旋转，应力合成和梁应变的三场变分公式。在Euler-Lagrange方程中，高阶应力合力设置为零。本文中的公式仅限于矩形横截面。束应变的插值包括两个部分。第一部分与应力合成插值相同。第二部分描述了截面翘曲，并允许横向法向应变。在这种方法中，可以轻松实现与任意三维本构律的接口。由于采用了混合插值技术，可以在梁单元的长度方向上应用高斯积分，从而获得无锁定单元的公式。通过几个数值例子证明了该方法的有效性。我们提出了弹性，非弹性和稳定性问题的结果，并评估了空间梁结构的承载能力。新元件的基本特征是在非线性应用中的鲁棒性。与其他元素配方相比，它允许非常大的载荷阶跃。

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