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Influence of spatially varying material properties on the bimoment normal and shear stresses by warping torsion of FGM beams

机译：通过FGM光束翘曲扭转对空间不同材料特性对Bimoment正常和剪切应力的影响

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摘要

In this contribution, which is an extension of author's research [1,2], an influence of the in two and three directions varying material properties on non-uniform torsion of the Functionally Graded Material (FGM) thin walled beams is originally investigated. Based on the semi-analytical solution of the fourth order differential equation for non-uniform torsion, the local finite element equations of the twisted FGM beam are presented, considering the non-uniform torsion with effect of warping and secondary deformations due to the angle of twist. The warping part of the first derivative of the twist angle caused by the bimoment is considered as an additional degree of freedom at the beam nodes. The Multi-Layers Method (MLM) [3], and the Reference Beam Method (RBM) [4] are extended for homogenization of the spatially varying material properties and relevant stiffnesses in the real beam onto effective longitudinally varying ones in the homogenized beam for the load case of non-uniform torsion.The focus of the numerical investigation, with consideration of the warping and Deformation Effect due to the Secondary Torsional Moment (STMDE), is on elastostatic analysis of straight FGM beams with rectangular hollow cross-sections. The influence of the variation of the material properties with respect to two or three directions on the angle of twist and the bimoment normal and torsional shear stresses is investigated. The obtained results are compared with the ones calculated by a very fine mesh of standard solid finite elements. This FGM warping non-uniform torsion beam finite element can be used not only in torsional analysis of general thin-walled beams but also in the design of FGM sensors and actuators in mechatronics.
机译：在这一贡献中，这是作者研究的延伸[1,2]，最初研究了在功能梯度薄壁梁的不均匀扭转上改变材料特性的两个和三个方向的影响。基于对不均匀扭转的四阶微分方程的半分析解决方案，提出了扭曲的FGM光束的局部有限元方程，考虑到由于角度而导致的翘曲和二次变形的效果的不均匀扭转捻。由Bimoment引起的扭曲角度的扭曲部分被认为是光束节点的额外自由度。多层方法（MLM）[3]和参考光束方法（RBM）[4]延伸以使空间变化的材料特性和实际光束中的相关刚度的均质化在均质化梁中的有效纵向变化的梁上不均匀扭转的载荷情况。数值调查的重点是考虑到由于次级扭转力矩（STMDE）引起的翘曲和变形效果，是用矩形中空横截面的直的FGM梁的弹性分析。研究了材料特性相对于扭曲角度和扭转剪切应力的两个或三个方向的影响。将得到的结果与由标准固体有限元的非常细网格计算的结果进行比较。该FGM翘曲的非均匀扭转梁有限元件不仅可以用于通用薄壁梁的扭转分析，而且可以在机电一体化中的FGM传感器和执行器的设计中使用。

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