南京理工大学学报（自然科学版）
南京理工大學學報（自然科學版）
남경리공대학학보（자연과학판）
JOURNAL OF NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY
2014年
1期
78-82
,共5页
轴向拉压应变%刚度矩阵%空间变截面梁%多体系统传递矩阵法
軸嚮拉壓應變%剛度矩陣%空間變截麵樑%多體繫統傳遞矩陣法
축향랍압응변%강도구진%공간변절면량%다체계통전체구진법
axial tension and compression strain%stiffness matrix%space non-uniform beam%transfer matrix method of multibody system
采用有限元法来推导了空间变截面梁单元的传递矩阵。在推导空间变截面梁单元的刚度矩阵时，在位移列阵中增加了一项位移值：轴向拉压应变，以提高位移插值函数的阶数。并采用高次多项式位移插值函数来推导空间变截面梁单元的刚度矩阵，然后通过矩阵变换得到该梁的传递矩阵。将得到的传递矩阵应用于悬臂梁，计算了悬臂梁的挠度和模态。研究结果表明：该方法可精确计算空间变截面梁的变形，并为联合有限元法和多体系统传递矩阵法求解复杂系统动力学问题提供一个新思路。
採用有限元法來推導瞭空間變截麵樑單元的傳遞矩陣。在推導空間變截麵樑單元的剛度矩陣時，在位移列陣中增加瞭一項位移值：軸嚮拉壓應變，以提高位移插值函數的階數。併採用高次多項式位移插值函數來推導空間變截麵樑單元的剛度矩陣，然後通過矩陣變換得到該樑的傳遞矩陣。將得到的傳遞矩陣應用于懸臂樑，計算瞭懸臂樑的撓度和模態。研究結果錶明：該方法可精確計算空間變截麵樑的變形，併為聯閤有限元法和多體繫統傳遞矩陣法求解複雜繫統動力學問題提供一箇新思路。
채용유한원법래추도료공간변절면량단원적전체구진。재추도공간변절면량단원적강도구진시，재위이렬진중증가료일항위이치：축향랍압응변，이제고위이삽치함수적계수。병채용고차다항식위이삽치함수래추도공간변절면량단원적강도구진，연후통과구진변환득도해량적전체구진。장득도적전체구진응용우현비량，계산료현비량적뇨도화모태。연구결과표명：해방법가정학계산공간변절면량적변형，병위연합유한원법화다체계통전체구진법구해복잡계통동역학문제제공일개신사로。
Transfer matrix of space non-uniform beam element is deduced using finite element method in this paper. When stiffness matrix of space non-uniform beam element is deduced,a new displacement named axial tension and compression strain is introduced to increase the degree of axial displacement interpolating function. Stiffness matrix of space non-uniform beam element is calculated according to higher-degree polynomial interpolating function, and transfer matrix of the beam is obtained by matrix transforming. The deflection and modal of beam are calculated based on the transfer matrix. The calculation results prove that this method has highly calculating precision,and it provides a new idea to solve the problem of complex system dynamics by combining finite element method and transfer matrix method of multibody system.
