含脱层层合简支梁屈曲问题的弹性力学解

BUCKLING ANALYSIS OF SIMPLY SUPPORTED DELAMINATED BEAMS BASED ON ELASTICITY THEORY

基于二维弹性力学理论,该文采用配点法研究轴向荷载作用下,含脱层复合材料层合简支梁的屈曲问题。首先,将层合梁沿层间界面切开,由弹性力学位移法,建立各单层梁的屈曲微分方程,分别求得各层梁的弹性力学解。其次,采用配点法将梁长等分,在层间界面上取与级数项数相等的点,将各匹配点处的界面方程与梁上下表面的边界方程联合求解,得到其屈曲临界载荷及屈曲形态。算例分析了脱层尺寸、脱层位置对层合简支梁屈曲性能的影响。将本文结果与梁理论结果进行了比较,对于细梁显示出很好的一致性,但对于粗梁,该文的弹性力学解要比梁理论解精确得多。

Based on the two-dimensional elasticity theory, the buckling of delaminated composite beams is investigated by means of the point collocation method. Firstly, according to the plane elasticity theory, the analytical solution of a piece of homogeneous beam is obtained, which satisfies the simply-supported conditions of the beam at both ends. Then, using the point collocation technique, the laminated beam is divided into equidistance along the interface of the beam. Taking the series numbers to be equal to the matching points, the buckling loads are obtained by means of the interface equations at every points as well as the upper and lower surface conditions of the beam. The numerical results show excellent convergence with high accuracy. The effects of delamination positions and delamination sizes on the critical buckling loads are investigated in details. The proposed solutions are compared with those from the classic beam theory based on plane section assumption, which is only valid for the slender beams. However, the proposed method is applicable to both slender beams and thick beams.