求解混凝土等效断裂韧度的小波基无单元方法

ELEMENT FREE GALERKIN METHOD WITH WAVELET BASIS FOR CALCULATING EQUIVALENT FRACTURE TOUGHNESS OF CONCRETE

考虑混凝土主裂缝亚临界扩展长度及虚拟裂缝区粘聚力,利用,积分与应力强度因子的解析关系,建立基于小波基无单元方法求解混凝土等效断裂韧度的数值方法,研究不同基底小波分辨率对混凝土等效断裂韧度计算值的影响。对8个带裂缝试件的混凝土等效断裂韧度的计算结果表明:在相同小波基分辨率下,4根体积系列试件的计算值的均方差和变异系数分别小于0.0244和0.0231,4根高度系列试件的计算值的均方差和变异系数分别小于0.0384和0.0362,计算结果的一致性好;与解析解相比,8个试件的计算值的最大相对误差均在5%左右,计算结果的精度高;且不同小波基分辨率对计算结果影响不大。由此得出结论,小波基无单元方法是求解混凝土等效断裂韧度的一种可靠的高精度数值方法,可以作为混凝土断裂力学的一种有力的计算工具。

Considering the length of the subcritical growth of the main crack and the cohesive strength of the fictitious crack of concrete, and using the analytical relationship between the J integral and the stress intensity factor, a numerical algorithm based on the element free Galerkin method with wavelet basis to solve the equivalent fracture toughness of concrete is proposed, and the influence of different resolutions of wavelet basis on the calculated values of the equivalent fracture toughness of concrete is investigated. The calculated results for the equivalent fracture toughness of concrete of 8 specimens with cracks show that in the case of the identical resolution of wavelet basis, the mean square deviations and the coefficients of variation of the calculated values of the 4 specimens with different volumes are smaller than 0.0244 and 0.0231, respectively, and the mean square deviations and the coefficients of variation of the calculated values of the 4 specimens with different heights are smaller than 0.0384 and 0.0362, so the consistency of the calculated results is satisfactory. By comparing with the analytical solutions, the maximum relative error of the calculated values of 8 specimens is about 5%, so the accuracy of the calculated results is high. And the influence of different resolutions of wavelet basis on the calculated results is small. A conclusion is given that the element free Galerkin method with wavelet basis is a reliable numerical algorithm with high precision to solve the equivalent fracture toughness of concrete, and may be taken as a powerful calculation tool in the fracture mechanics of concrete.