基于精细梁模型的向量式有限元分析
Vector form intrinsic finite element analysis based on fine beam model

精细梁不同于Euler梁和Timoshenko梁，该模型在考虑剪切变形的同时还考虑了横向弯曲时截面转动产生的附加轴向位移及横向剪切变形影响截面抗弯刚度后产生的附加横向位移。推导了适用于向量式有限元分析的精细梁单元应变和内力表达式，采用FORTRAN自编了向量式有限元程序。对悬臂梁、两端固支梁和门式框架进行了算例分析，对比了采用不同梁单元模型下结构的竖向位移。结果表明：当高跨比较小时，3种梁单元的竖向位移相差不大；当高跨比较大时，精细梁单元的竖向位移较Euler梁和Timoshenko梁明显增大，表明剪切变形及刚度折减引起的附加轴向位移、附加横向位移不能忽略。精细梁单元模型对高跨比较大的梁进行分析可望得到更精确的结果。
The proposed fine beam model is different from that of Euler beam and Timoshenko beam. Some effects were considered in the new model such as shear displacement，the additional axial displacement produced by lateral bending and the additional transverse displacement produced by reduced stiffness due to transverse shear deformation. The formula of strain and internal force of the fine beam model，applied to Vector Form Intrinsic Finite Element (VFIFE) analysis，were derived and corresponding programs were developed by Fortran language. Cantilever beam，both ends clamped beam and portal frame are analyzed and the vertical displacements were compared using different beam element models. Numerical results showed that when the depth-span ratio was relatively small，the vertical displacements obtained by different beam model had slight difference. When the depth-span ratio was larger，the vertical displacement obtained by the fine beam model was obviously larger than that obtained by the Euler beam and Timoshenko beam. Therefore，the shear displacement，the additional axial displacement and the additional transverse displacement caused by stiffness reduction should not be ignored when the deep beam was analyzed. The new beam model proposed in this paper demonstrated more accurate results when the beam had a large depth-span ratio.