Efficient and reliable solutions of static and dynamic nonlinear structural mechanics problems by an integrated numerical approach using DQFEM and direct time integration with accelerated equilibrium iteration schemes
Integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM) which uses the differential quadrature (DQ) techniques to the finite element discretization is used to analyze...
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| Vydané v: | Applied mathematical modelling Ročník 24; číslo 8; s. 637 - 655 |
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| Jazyk: | English |
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01.07.2000
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| ISSN: | 0307-904X |
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| Abstract | Integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM) which uses the differential quadrature (DQ) techniques to the finite element discretization is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor–corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm. |
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| AbstractList | Integrated numerical techniques for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM), which uses the differential quadrature (DQ) techniques for the finite element discretization, is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor-corrector equilibrium iterations, which are efficient and reliable, are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm. Integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM) which uses the differential quadrature (DQ) techniques to the finite element discretization is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor–corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm. |
| Author | Chen, C.-N |
| Author_xml | – sequence: 1 givenname: C.-N surname: Chen fullname: Chen, C.-N email: cchen@mail.ncku.edu.tw organization: Department of Naval Architecture and Marine Engineering, National Cheng Kung University, Tainan, Taiwan, ROC |
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| Cites_doi | 10.1115/1.2900803 10.1016/0045-7949(94)00328-Z 10.1002/nme.1620151011 10.1061/JMCEA3.0000098 10.1016/0022-247X(71)90110-7 10.1002/nme.1620350304 10.1002/eqe.4290050306 10.1016/0045-7949(84)90059-2 |
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| Keywords | Global secant relaxation Parallel implementation DQFEM Accelerated constant stiffness iteration Explicit predictor–corrector iteration |
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| References | Bellman, Casti (BIB5) 1971; 34 C.N. Chen, A differential quadrature finite difference method, in: Proceedings of the International Conference on Adv. Comput. Meth. Engr., Ghent, Belgium, 1998, pp. 713–720 J.P. Ponthot, M. Hogge, On relative merits of implicit/explicit algorithms for transient problems in metal forming simulation, in: Proceedings of the International Conference on Numerical Methods for Metal Forming in Industry, Baden–Baden, GERMANY, vol. 2, 1994, pp. 128–148 C.N. Chen, A generalized differential quadrature element method, in: Proceedings of the International Conference on Adv. Comput. Meth. Engr., Ghent, Belgium, 1998, pp. 721–728 C.N. Chen, The differential quadrature finite element method, in: D. Pamplona et al. (Eds.), Applied Mechanics in the Americas, American Academy of Mechanics, vol. 6, 1998, pp. 309–312 Chen (BIB18) 1995; 54 C.N. Chen, Newton-Raphson techniques in finite element methods for non-linear structural problems, one chapter in GORDON and BREACH International Series in Engineering, Technology and Applied Science, Volumes on Structural Dynamic Systems Computational Techniques and Optimization C.T. Leondes (Ed.), Gordon and Breach, 1998 Hodge (BIB19) 1959 C.N. Chen, Extended differential quadrature, in: Applied Mechanics in the Americas, in: D. Pamplona et al. (Eds.), American Academy of Mechanics 6, 1998, pp. 389–392 Chung, Hulbert (BIB10) 1993; 60 N.M. Newmark, A method of computation for structural dynamics, in: Proceedings of the Amer. Soc. Civ. Engrg. 85, EM3, 1959, pp. 67–94 Wood, Bossak, Zienkiewicz (BIB12) 1980; 15 E. Cahill, Acceleration techniques for functional iteration of non-linear equations, in IMACS Conference on Mathematical Modelling and Scientific Computing, Bangalove, India, 1992 C.N. Chen, A differential quadrature element method, in: Proceedings of the First International Conference on Engineering Computation and Computer Simulation, Changsha, China, vol. 1, 1995, pp. 25–34 M. Hogge, J.P. Ponthot, Efficient implicit schemes for transient problems in metal forming simulation, Numerical and Physical Study of Material Forming Processes, Paris, France, 1996 C.N. Chen, Improved constant stiffness algorithms for the finite element analysis, in: Proceedings of the NUMETA 90, Swansea, UK, 1990, pp. 623–628 Hilber, Hughes, Taylor (BIB11) 1977; 5 Chen (BIB2) 1992; 35 Crisfield (BIB17) 1984; 18 Crisfield (10.1016/S0307-904X(00)00007-X_BIB17) 1984; 18 10.1016/S0307-904X(00)00007-X_BIB8 10.1016/S0307-904X(00)00007-X_BIB9 Bellman (10.1016/S0307-904X(00)00007-X_BIB5) 1971; 34 10.1016/S0307-904X(00)00007-X_BIB6 Chung (10.1016/S0307-904X(00)00007-X_BIB10) 1993; 60 10.1016/S0307-904X(00)00007-X_BIB7 Hilber (10.1016/S0307-904X(00)00007-X_BIB11) 1977; 5 10.1016/S0307-904X(00)00007-X_BIB4 10.1016/S0307-904X(00)00007-X_BIB3 Chen (10.1016/S0307-904X(00)00007-X_BIB2) 1992; 35 10.1016/S0307-904X(00)00007-X_BIB1 Chen (10.1016/S0307-904X(00)00007-X_BIB18) 1995; 54 10.1016/S0307-904X(00)00007-X_BIB13 Hodge (10.1016/S0307-904X(00)00007-X_BIB19) 1959 Wood (10.1016/S0307-904X(00)00007-X_BIB12) 1980; 15 10.1016/S0307-904X(00)00007-X_BIB14 10.1016/S0307-904X(00)00007-X_BIB15 10.1016/S0307-904X(00)00007-X_BIB16 |
| References_xml | – reference: N.M. Newmark, A method of computation for structural dynamics, in: Proceedings of the Amer. Soc. Civ. Engrg. 85, EM3, 1959, pp. 67–94 – reference: C.N. Chen, A generalized differential quadrature element method, in: Proceedings of the International Conference on Adv. Comput. Meth. Engr., Ghent, Belgium, 1998, pp. 721–728 – volume: 60 start-page: 371 year: 1993 end-page: 375 ident: BIB10 article-title: A time integration algorithm for structural dynamics with improved numerical dissipations: the generalized- publication-title: J. Appl. Mech. – volume: 54 start-page: 199 year: 1995 end-page: 205 ident: BIB18 article-title: A global secant relaxation (GSR) method-based predictor–corrector procedure for the iterative solution of finite element systems publication-title: Comput. Struct. – reference: C.N. Chen, Extended differential quadrature, in: Applied Mechanics in the Americas, in: D. Pamplona et al. (Eds.), American Academy of Mechanics 6, 1998, pp. 389–392 – year: 1959 ident: BIB19 publication-title: Plastic Analysis of Structures – reference: M. Hogge, J.P. Ponthot, Efficient implicit schemes for transient problems in metal forming simulation, Numerical and Physical Study of Material Forming Processes, Paris, France, 1996 – volume: 5 start-page: 283 year: 1977 end-page: 292 ident: BIB11 article-title: Improved numerical dissipation for time integration algorithms in structural dynamics publication-title: Earthquake Engrg. Struct. Dynamics – volume: 34 start-page: 235 year: 1971 end-page: 238 ident: BIB5 article-title: Differential quadrature and long-term integration publication-title: J. Math. Anal. Appl. – reference: C.N. Chen, A differential quadrature element method, in: Proceedings of the First International Conference on Engineering Computation and Computer Simulation, Changsha, China, vol. 1, 1995, pp. 25–34 – volume: 35 start-page: 481 year: 1992 end-page: 490 ident: BIB2 article-title: Efficient and reliable accelerated constant stiffness algorithms for the solution of non-linear problems publication-title: Int. J. Numer. Meth. Engrg. – reference: E. Cahill, Acceleration techniques for functional iteration of non-linear equations, in IMACS Conference on Mathematical Modelling and Scientific Computing, Bangalove, India, 1992 – reference: C.N. Chen, Newton-Raphson techniques in finite element methods for non-linear structural problems, one chapter in GORDON and BREACH International Series in Engineering, Technology and Applied Science, Volumes on Structural Dynamic Systems Computational Techniques and Optimization C.T. Leondes (Ed.), Gordon and Breach, 1998 – reference: C.N. Chen, Improved constant stiffness algorithms for the finite element analysis, in: Proceedings of the NUMETA 90, Swansea, UK, 1990, pp. 623–628 – volume: 18 start-page: 267 year: 1984 end-page: 278 ident: BIB17 article-title: Accelerated and damping the modified Newton-Raphson method publication-title: Comput. Struct. – volume: 15 start-page: 1562 year: 1980 end-page: 1566 ident: BIB12 article-title: An alpha modification of Newmark's method publication-title: Int. J. Numer. Meth. Engrg. – reference: C.N. Chen, The differential quadrature finite element method, in: D. Pamplona et al. (Eds.), Applied Mechanics in the Americas, American Academy of Mechanics, vol. 6, 1998, pp. 309–312 – reference: C.N. Chen, A differential quadrature finite difference method, in: Proceedings of the International Conference on Adv. Comput. Meth. Engr., Ghent, Belgium, 1998, pp. 713–720 – reference: J.P. Ponthot, M. Hogge, On relative merits of implicit/explicit algorithms for transient problems in metal forming simulation, in: Proceedings of the International Conference on Numerical Methods for Metal Forming in Industry, Baden–Baden, GERMANY, vol. 2, 1994, pp. 128–148 – ident: 10.1016/S0307-904X(00)00007-X_BIB1 – ident: 10.1016/S0307-904X(00)00007-X_BIB3 – volume: 60 start-page: 371 year: 1993 ident: 10.1016/S0307-904X(00)00007-X_BIB10 article-title: A time integration algorithm for structural dynamics with improved numerical dissipations: the generalized-α method publication-title: J. Appl. Mech. doi: 10.1115/1.2900803 – year: 1959 ident: 10.1016/S0307-904X(00)00007-X_BIB19 – volume: 54 start-page: 199 year: 1995 ident: 10.1016/S0307-904X(00)00007-X_BIB18 article-title: A global secant relaxation (GSR) method-based predictor–corrector procedure for the iterative solution of finite element systems publication-title: Comput. Struct. doi: 10.1016/0045-7949(94)00328-Z – volume: 15 start-page: 1562 year: 1980 ident: 10.1016/S0307-904X(00)00007-X_BIB12 article-title: An alpha modification of Newmark's method publication-title: Int. J. Numer. Meth. Engrg. doi: 10.1002/nme.1620151011 – ident: 10.1016/S0307-904X(00)00007-X_BIB13 doi: 10.1061/JMCEA3.0000098 – volume: 34 start-page: 235 year: 1971 ident: 10.1016/S0307-904X(00)00007-X_BIB5 article-title: Differential quadrature and long-term integration publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(71)90110-7 – volume: 35 start-page: 481 year: 1992 ident: 10.1016/S0307-904X(00)00007-X_BIB2 article-title: Efficient and reliable accelerated constant stiffness algorithms for the solution of non-linear problems publication-title: Int. J. Numer. Meth. Engrg. doi: 10.1002/nme.1620350304 – ident: 10.1016/S0307-904X(00)00007-X_BIB6 – ident: 10.1016/S0307-904X(00)00007-X_BIB7 – ident: 10.1016/S0307-904X(00)00007-X_BIB4 – ident: 10.1016/S0307-904X(00)00007-X_BIB8 – ident: 10.1016/S0307-904X(00)00007-X_BIB9 – volume: 5 start-page: 283 year: 1977 ident: 10.1016/S0307-904X(00)00007-X_BIB11 article-title: Improved numerical dissipation for time integration algorithms in structural dynamics publication-title: Earthquake Engrg. Struct. Dynamics doi: 10.1002/eqe.4290050306 – ident: 10.1016/S0307-904X(00)00007-X_BIB16 – volume: 18 start-page: 267 year: 1984 ident: 10.1016/S0307-904X(00)00007-X_BIB17 article-title: Accelerated and damping the modified Newton-Raphson method publication-title: Comput. Struct. doi: 10.1016/0045-7949(84)90059-2 – ident: 10.1016/S0307-904X(00)00007-X_BIB14 – ident: 10.1016/S0307-904X(00)00007-X_BIB15 |
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| SubjectTerms | Accelerated constant stiffness iteration DQFEM Explicit predictor–corrector iteration Global secant relaxation Parallel implementation |
| Title | Efficient and reliable solutions of static and dynamic nonlinear structural mechanics problems by an integrated numerical approach using DQFEM and direct time integration with accelerated equilibrium iteration schemes |
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