In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of ...In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.展开更多
The new hybrid elements are proposed by combing modified Hermitian wavelet elements with ANASYS elements. Then hybrid elements are substituted into finite element formulations to solve the load identification. Transfe...The new hybrid elements are proposed by combing modified Hermitian wavelet elements with ANASYS elements. Then hybrid elements are substituted into finite element formulations to solve the load identification. Transfer matrix can be constructed by using the inverse Newmark algorithm and hybrid finite element method. Loads can obtain through the responses and the transfer matrix. Load identification law was studied under different excitation cases in rod and Timoshenko beam.Regularization method is adopted to solve ill-posed inverse problem of load identification. Compared with ANSYS results,hybrid elements and HCSWI elements can accurately identify the applied load. Numerical results show that the algorithm of hybrid elements is effective. The accuracy of hybrid elements and HCSWI elements can be verified by comparing the load identification result of ANASYS elements with the experiment data. Hermitian wavelet finite element methods have high accuracy advantage but it is difficult to apply the engineering practice. In practical engineering, complex structure can be analyzed by using the hybrid finite element methods which can be obtained the high accuracy in the crucial component.展开更多
基金Supported by the Natural Science Foundation of Henan（0211044800）
文摘In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.51421004&51405370)the National Basic Research Program of China(Grant No.2015CB057400)+1 种基金the Natural Science Basic Plan in Shaanxi Province of China(Grant No.2015JQ5184)Project Funded by China Postdoctoral Science Foundation(Grant No.2016T90908)
文摘The new hybrid elements are proposed by combing modified Hermitian wavelet elements with ANASYS elements. Then hybrid elements are substituted into finite element formulations to solve the load identification. Transfer matrix can be constructed by using the inverse Newmark algorithm and hybrid finite element method. Loads can obtain through the responses and the transfer matrix. Load identification law was studied under different excitation cases in rod and Timoshenko beam.Regularization method is adopted to solve ill-posed inverse problem of load identification. Compared with ANSYS results,hybrid elements and HCSWI elements can accurately identify the applied load. Numerical results show that the algorithm of hybrid elements is effective. The accuracy of hybrid elements and HCSWI elements can be verified by comparing the load identification result of ANASYS elements with the experiment data. Hermitian wavelet finite element methods have high accuracy advantage but it is difficult to apply the engineering practice. In practical engineering, complex structure can be analyzed by using the hybrid finite element methods which can be obtained the high accuracy in the crucial component.
