A three-dimensional extended finite element method (X-FEM) coupled with a narrow band fast marching method (FMM) is developed and implemented in the Abaqus finite element package for curvilinear fatigue crack growth and life prediction analysis of metallic structures. Given the level set representation of arbitrary crack geometry, the narrow band FMM provides an efficient way to update the level set values of its evolving crack front. In order to capture the plasticity induced crack closure effect, an element partition and state recovery algorithm for dynamically allocated Gauss points is adopted for efficient integration of historical state variables in the near-tip plastic zone. An element-based penalty approach is also developed to model crack closure and friction. The proposed technique allows arbitrary insertion of initial cracks, independent of a base 3D model, and allows non-self-similar crack growth pattern without conforming to the existing mesh or local remeshing. Several validation examples are presented to demonstrate the extraction of accurate stress intensity factors for both static and growing cracks. Fatigue life prediction of a flawed helicopter lift frame under the ASTERIX spectrum load is presented to demonstrate the analysis procedure and capabilities of the method.
Abstract-In this paper, the construction method of common measurement matrices is studied, adaptability of common measurement matrices for mechanical vibration signal is analyzed. Typical measurement matrices are selected from commonly used measurement matrices, Gaussian random measurement matrix and Bernoulli random measurement matrix are chosen from totally random measurement matrices, Circulant measurement matrix and Toeplitz measurement matrix are selected from deterministic matrices, partially random Fourier measurement matrix and Hadamard matrix are chosen from deterministic measurement matrices. The sensing performance of common measurement matrices for mechanical vibration signal is evaluated from the two perspective of reconstruction error and memory space. The simulation results show that two kinds of complete random matrices, Gaussian and Bernoulli matrices, can exactly reconstruct original vibration signal, but they occupy large memory space; deterministic matrices, Circulant and Toeplitz matrices, although need fewer memory space, obtained measurements which do not have information of global vibration signal lead to lower reconstruction results; partially random Fourier matrix is extremely coherent with sparse transforming base of vibration signal, so it has not exact result in the process of reconstructing original vibration signal, the requirement of Exponentiation of 2 seriously restrict its application.
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