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Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load
https://orcid.org/http://orcid.org/0000-0002-7121-5637
The dynamic finite element analysis of truss with multi freedom nonlinear constraints requires the implementation of constraints to producing the modified dynamic system of equations. Generally, in finite element analysis the mathematical technique for imposing nonlinear boundary constraints based on optimization methods such as the penalty augmentation method and Lagrange multiplier adjunction method. This paper presents an approach to treat the nonlinear multi freedom constraints in dynamic finite element analysis of truss based on the Lagrange multiplier method. Using the Lagrange multiplier method the modified dynamic equilibrium equation is constructed by extremizing the Hamiltonian function and converting a constrained problem into an unconstrained problem. To solve the dynamic equilibrium equation of system under time-dependent harmonic force, the algorithm is established based on the combining Newmark integration method and Newton Raphson method. Using the proposed algorithm the calculation program for dynamic analysis of truss subjected to harmonic load is written. The illustration of numerical example shows the efficiency of the established algorithm.
Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load
https://orcid.org/http://orcid.org/0000-0002-7121-5637
The dynamic finite element analysis of truss with multi freedom nonlinear constraints requires the implementation of constraints to producing the modified dynamic system of equations. Generally, in finite element analysis the mathematical technique for imposing nonlinear boundary constraints based on optimization methods such as the penalty augmentation method and Lagrange multiplier adjunction method. This paper presents an approach to treat the nonlinear multi freedom constraints in dynamic finite element analysis of truss based on the Lagrange multiplier method. Using the Lagrange multiplier method the modified dynamic equilibrium equation is constructed by extremizing the Hamiltonian function and converting a constrained problem into an unconstrained problem. To solve the dynamic equilibrium equation of system under time-dependent harmonic force, the algorithm is established based on the combining Newmark integration method and Newton Raphson method. Using the proposed algorithm the calculation program for dynamic analysis of truss subjected to harmonic load is written. The illustration of numerical example shows the efficiency of the established algorithm.
Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load
https://orcid.org/http://orcid.org/0000-0002-7121-5637
The dynamic finite element analysis of truss with multi freedom nonlinear constraints requires the implementation of constraints to producing the modified dynamic system of equations. Generally, in finite element analysis the mathematical technique for imposing nonlinear boundary constraints based on optimization methods such as the penalty augmentation method and Lagrange multiplier adjunction method. This paper presents an approach to treat the nonlinear multi freedom constraints in dynamic finite element analysis of truss based on the Lagrange multiplier method. Using the Lagrange multiplier method the modified dynamic equilibrium equation is constructed by extremizing the Hamiltonian function and converting a constrained problem into an unconstrained problem. To solve the dynamic equilibrium equation of system under time-dependent harmonic force, the algorithm is established based on the combining Newmark integration method and Newton Raphson method. Using the proposed algorithm the calculation program for dynamic analysis of truss subjected to harmonic load is written. The illustration of numerical example shows the efficiency of the established algorithm.
Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load
Lecture Notes in Civil Engineering
Akimov, Pavel (Herausgeber:in) / Vatin, Nikolai (Herausgeber:in) / Quyen, Vu Thi Bich (Autor:in) / Tien, Dao Ngoc (Autor:in) / Van, Tran Thi Thuy (Autor:in) / Van Dat, Pham (Autor:in)
International Conference on Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering ; 2021 ; Moscow, Russia
XXX Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP 2021) ; Kapitel: 34 ; 290-299
15.09.2021
10 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Multi freedom constraint , Lagrange multiplier method , Nonlinear boundary constraints , Imposing nonlinear constraint , Dynamic finite element analysis of truss Engineering , Building Construction and Design , Geotechnical Engineering & Applied Earth Sciences , Transportation Technology and Traffic Engineering , Structural Materials