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首页> 外文期刊>Journal of Biomechanics >2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones.
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2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones.

机译：基于复合梁理论的二维计算方法，用于确定长骨的局部均质刚度。

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摘要

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.
机译：提出了一种使用有限元技术的计算方法。它的主要目的是确定胫骨任何横截面的应变，应力，尤其是刚度，从而使胫骨扭转在体内得以定位。每个胫骨横截面被认为是具有任意纤维取向的复合梁的不均匀横截面。通过解决变分问题，可以确定复合梁截面内的应力，应变和刚度的确定。该方法的验证是在胫骨骨干上进行的，假设每个横截面都是由正交异性材料制成的复合梁的横截面，且正交异性轴相对于骨骼主轴的方向都不同。由于无法通过实验获得局部刚度，因此对网格截面的每个节点值（应变，应力）进行了模型和三维模型结果的比较。结果之间的良好一致性验证了我们的有限元程序。实际上，该方法已能够以较高的准确度直接处理来自CT扫描图像的2D几何重建，从而可以局部确定体内胫骨的均质力学特征，尤其是在不近似十字形的情况下量化儿童的胫骨扭转畸形截面和通过计算实际的惯性矩J来强调纤维取向相对于刚度值的重要性。这种2D方法还允许减少3D建模和计算的CPU时间。

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