含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析

该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案，实施微裂纹损伤诱发截面弱化，实现多裂纹深度、位置、数目的模拟。引入变截面Timoshenko梁的h型有限元网格自适应分析方法，求解含裂纹损伤圆弧曲梁自由振动问题，得到优化的网格和满足预设误差限的高精度自振频率和振型解答，研究多裂纹损伤对圆弧曲梁振型的扰动行为。数值算例表明，该算法中网格非均匀加密可适应裂纹损伤引起的振型变化，应用于各类曲梁夹角和裂纹损伤分布工况下的自由振动研究，定量分析了多裂纹损伤深度、数目、分布对圆弧曲梁自振频率和振型的扰动影响，检验了该文算法的精确性和实用性。

ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR FREE VIBRATION DISTURBANCE OF CIRCULARLY CURVED BEAMS WITH MULTIPLE CRACKS

The scheme for the cross-section damage defects in a circularly curved beam is established to simulate the depth, the location and the number of multiple cracks, through implementing cross-section reduction induced by microcrack damage. The h-version adaptive finite element method of a variable cross-section Timoshenko beam is introduced to solve the free vibration of a circularly curved beam with cracks damage. Using the proposed method, the final optimized meshes and high-precision solution of natural frequency and mode shape satisfying the preset error tolerance can be obtained, and the disturbance behavior of multi crack damage on the vibration mode of a circularly curved beam is studied. Numerical examples show that the non-uniform mesh refinement can adapt to the change of mode of vibration induced by crack damage, which is applied to the free vibration research of various circularly curved beams with included angles and crack damage distribution conditions. Furthermore, the influences of crack damage depth, crack damage number, and crack damage distribution on the natural frequency and mode of vibration of a circularly curved beam are quantitatively analyzed, and the accuracy and practicability of the proposed algorithm are verified.