A CONTINUOUS STIFFNESS APPROACH FOR MODELING EDGE-CRACKED BEAMS WITH DIFFERENT CROSS-SECTIONS BASED ON ENERGY THEORY

摘要

The distribution of flexibility and bending stiffness of beams is altered by the crack size and location, the shape of beam cross-section, and the beam length. However, up to now, most of the studies are mainly on the solid rectangular section beams, rarely on the beams with variable cross-sections. A novel continuous stiffness methodology for four classical cross-section beams is proposed based on fracture mechanics and energy theory to estimate the effects of edge-crack depth and location and the shape of cross-section on the distribution of bending stiffness. First, the continuous bending stiffness of beams with shallow and deep cracks is derived and solved using the Newton-Raphson technique. The extent and degree of influence of crack depth, crack location, beam's length, and beam's cross-section on the distribution of bending stiffness are studied. Second, the correctness of the proposed continuous stiffness method is verified using the experimental and theoretical data and the results of the solid rectangular section beams in the literature. Finally, the natural frequency ratios of the beams with different cross-sections, crack depths, crack positions, and beam lengths are studied in detail using the precious integration method (PIM), ANSYS element modeling (AEM) method, ANSYS solid modeling (ASM) method, and Rotational Spring Modeling (RSM), respectively. The availability and reliability of the proposed approach are verified further. The study of the proposed continuous stiffness method may provide some valuable references for modeling cracks of the different cross-section beams.