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Beam structure is one of the most widely used structures in mechanicalengineering and civil engineering. Ultrasonic guided wave based crackidentification is one of the most important and accepted approaches applied todetect unseen small flaws in structures. Numerical simulations of ultrasonicguided wave propagation have caught more and more attention due to the fastdevelopment of hardware and software in the last few years. From all thenumerical simulation methods, wavelet based finite element method has beenproved to be one of the most efficient methods due to its better spatialresolution, which means it needs fewer elements to get the same accuracy and itcan improve the calculation cost significantly. However, it needs a very smalltime interval. Laplace transform can easily convert the time domain into afrequency domain and then revert it back to a time domain. Laplace transformhas thus the advantage of finding better results with a very large timeinterval. which can save a lot of time cost. This paper will present aninnovative method combining Laplace transform and the B-spline wavelet oninterval (BSWI) finite element method. This novel method allows to get resultswith the same accuracy and with a significantly lower time cost, which wouldnot only decrease the total number of elements in the structure but alsoincrease the time integration interval. The numerical Laplace transform andBSWI finite element will be introduced. Moreover, this innovative method isapplied to simulate the ultrasonic wave propagation in a beam structure indifferent materials. Numerical examples for crack identification in beamstructures have been studied for verification.

Crack detection in beam structures with a novel Laplace based Wavelet Finite Element method