Augmented Numerical Manifold Method with implementation of flat-top partition of unity
This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Mor...
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Gespeichert in:
| Autor*in: |
He, Lei [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Schlagwörter: |
Finite element partition of unity |
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| Umfang: |
19 |
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| Übergeordnetes Werk: |
Enthalten in: LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS - Cundrle, Ivan ELSEVIER, 2013, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:61 ; year:2015 ; pages:153-171 ; extent:19 |
| Links: |
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| DOI / URN: |
10.1016/j.enganabound.2015.07.009 |
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ELV034692355 |
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| 520 | |a This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. | ||
| 520 | |a This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. | ||
| 650 | 7 | |a Linear dependence problem |2 Elsevier | |
| 650 | 7 | |a Flat-top partition of unity |2 Elsevier | |
| 650 | 7 | |a Finite element partition of unity |2 Elsevier | |
| 650 | 7 | |a High-order polynomial approximation |2 Elsevier | |
| 650 | 7 | |a Numerical manifold method |2 Elsevier | |
| 700 | 1 | |a An, Xinmei |4 oth | |
| 700 | 1 | |a Liu, Xiaoying |4 oth | |
| 700 | 1 | |a Zhao, Zhiye |4 oth | |
| 700 | 1 | |a Yang, Shengqi |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier Science |a Cundrle, Ivan ELSEVIER |t LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS |d 2013 |g Amsterdam [u.a.] |w (DE-627)ELV011629568 |
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10.1016/j.enganabound.2015.07.009 doi GBVA2015016000014.pica (DE-627)ELV034692355 (ELSEVIER)S0955-7997(15)00168-X DE-627 ger DE-627 rakwb eng 690 620 690 DE-600 620 DE-600 610 VZ 600 690 VZ 51.00 bkl 51.32 bkl He, Lei verfasserin aut Augmented Numerical Manifold Method with implementation of flat-top partition of unity 2015transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. Linear dependence problem Elsevier Flat-top partition of unity Elsevier Finite element partition of unity Elsevier High-order polynomial approximation Elsevier Numerical manifold method Elsevier An, Xinmei oth Liu, Xiaoying oth Zhao, Zhiye oth Yang, Shengqi oth Enthalten in Elsevier Science Cundrle, Ivan ELSEVIER LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS 2013 Amsterdam [u.a.] (DE-627)ELV011629568 volume:61 year:2015 pages:153-171 extent:19 https://doi.org/10.1016/j.enganabound.2015.07.009 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.00 Werkstoffkunde: Allgemeines VZ 51.32 Werkstoffmechanik VZ AR 61 2015 153-171 19 045F 690 |
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10.1016/j.enganabound.2015.07.009 doi GBVA2015016000014.pica (DE-627)ELV034692355 (ELSEVIER)S0955-7997(15)00168-X DE-627 ger DE-627 rakwb eng 690 620 690 DE-600 620 DE-600 610 VZ 600 690 VZ 51.00 bkl 51.32 bkl He, Lei verfasserin aut Augmented Numerical Manifold Method with implementation of flat-top partition of unity 2015transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. Linear dependence problem Elsevier Flat-top partition of unity Elsevier Finite element partition of unity Elsevier High-order polynomial approximation Elsevier Numerical manifold method Elsevier An, Xinmei oth Liu, Xiaoying oth Zhao, Zhiye oth Yang, Shengqi oth Enthalten in Elsevier Science Cundrle, Ivan ELSEVIER LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS 2013 Amsterdam [u.a.] (DE-627)ELV011629568 volume:61 year:2015 pages:153-171 extent:19 https://doi.org/10.1016/j.enganabound.2015.07.009 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.00 Werkstoffkunde: Allgemeines VZ 51.32 Werkstoffmechanik VZ AR 61 2015 153-171 19 045F 690 |
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10.1016/j.enganabound.2015.07.009 doi GBVA2015016000014.pica (DE-627)ELV034692355 (ELSEVIER)S0955-7997(15)00168-X DE-627 ger DE-627 rakwb eng 690 620 690 DE-600 620 DE-600 610 VZ 600 690 VZ 51.00 bkl 51.32 bkl He, Lei verfasserin aut Augmented Numerical Manifold Method with implementation of flat-top partition of unity 2015transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. Linear dependence problem Elsevier Flat-top partition of unity Elsevier Finite element partition of unity Elsevier High-order polynomial approximation Elsevier Numerical manifold method Elsevier An, Xinmei oth Liu, Xiaoying oth Zhao, Zhiye oth Yang, Shengqi oth Enthalten in Elsevier Science Cundrle, Ivan ELSEVIER LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS 2013 Amsterdam [u.a.] (DE-627)ELV011629568 volume:61 year:2015 pages:153-171 extent:19 https://doi.org/10.1016/j.enganabound.2015.07.009 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.00 Werkstoffkunde: Allgemeines VZ 51.32 Werkstoffmechanik VZ AR 61 2015 153-171 19 045F 690 |
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10.1016/j.enganabound.2015.07.009 doi GBVA2015016000014.pica (DE-627)ELV034692355 (ELSEVIER)S0955-7997(15)00168-X DE-627 ger DE-627 rakwb eng 690 620 690 DE-600 620 DE-600 610 VZ 600 690 VZ 51.00 bkl 51.32 bkl He, Lei verfasserin aut Augmented Numerical Manifold Method with implementation of flat-top partition of unity 2015transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. Linear dependence problem Elsevier Flat-top partition of unity Elsevier Finite element partition of unity Elsevier High-order polynomial approximation Elsevier Numerical manifold method Elsevier An, Xinmei oth Liu, Xiaoying oth Zhao, Zhiye oth Yang, Shengqi oth Enthalten in Elsevier Science Cundrle, Ivan ELSEVIER LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS 2013 Amsterdam [u.a.] (DE-627)ELV011629568 volume:61 year:2015 pages:153-171 extent:19 https://doi.org/10.1016/j.enganabound.2015.07.009 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.00 Werkstoffkunde: Allgemeines VZ 51.32 Werkstoffmechanik VZ AR 61 2015 153-171 19 045F 690 |
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10.1016/j.enganabound.2015.07.009 doi GBVA2015016000014.pica (DE-627)ELV034692355 (ELSEVIER)S0955-7997(15)00168-X DE-627 ger DE-627 rakwb eng 690 620 690 DE-600 620 DE-600 610 VZ 600 690 VZ 51.00 bkl 51.32 bkl He, Lei verfasserin aut Augmented Numerical Manifold Method with implementation of flat-top partition of unity 2015transfer abstract 19 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. Linear dependence problem Elsevier Flat-top partition of unity Elsevier Finite element partition of unity Elsevier High-order polynomial approximation Elsevier Numerical manifold method Elsevier An, Xinmei oth Liu, Xiaoying oth Zhao, Zhiye oth Yang, Shengqi oth Enthalten in Elsevier Science Cundrle, Ivan ELSEVIER LEPTIN CONCENTRATION PREDICTS CENTRAL SLEEP APNEA IN HEART FAILURE PATIENTS 2013 Amsterdam [u.a.] (DE-627)ELV011629568 volume:61 year:2015 pages:153-171 extent:19 https://doi.org/10.1016/j.enganabound.2015.07.009 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 51.00 Werkstoffkunde: Allgemeines VZ 51.32 Werkstoffmechanik VZ AR 61 2015 153-171 19 045F 690 |
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Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. 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The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. 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Augmented Numerical Manifold Method with implementation of flat-top partition of unity |
| abstract |
This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. |
| abstractGer |
This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. |
| abstract_unstemmed |
This paper formulates the flat-top partition of unity (PU)-based numerical manifold method (NMM). Through modifying the finite element PU into the flat-top PU, the linear dependence problem involved in finite element PU-based high-order polynomial approximations has been successfully alleviated. Moreover, the procedure to construct the flat-top PU is substantially simplified by taking full advantage of the unique features of the NMM, compared to that in other flat-top PU-based methods. The proposed method could also be treated as an improved version of the discontinuous deformation analysis (DDA) by completely avoiding the additional strategies previously used to enforce the displacement compatibility between adjacent elements. The formulations are presented in details for 1-D, 2-D and 3-D cases. The discrete equations of the flat-top PU-based NMM are derived based on the minimum potential energy principle. The simplex integration technique and its variation are employed to evaluate the integration of the matrices of the discrete equations over arbitrarily shaped manifold elements. Seven representative examples have validated the proposed method in the aspects of approximation accuracy and efficiency. |
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