Open AccessThe Eigensolution Expansion in Viscoelastic Materials
Author(s) -
Weixin Zhang,
LM Yang
Publication year - 2020
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.179
H-Index - 26
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/560/1/012022
Subject(s) - symplectic geometry , variable (mathematics) , mathematics , euclidean geometry , elasticity (physics) , mechanical system , hamiltonian system , hamiltonian (control theory) , mathematical analysis , classical mechanics , geometry , computer science , physics , mathematical optimization , artificial intelligence , thermodynamics
By using the eigensolution expansion method, the problem can be transformed into a Hamiltonian matrix. In symplectic system, the study of elasticity takes the primal variable and its dual variable as the basic variable, which makes the separated variable method be implemented smoothly, thus forming a unique direct method. The significance of the transition from Lagrangian system to Hamiltonian system lies in the transition from the traditional Euclidean geometry to the symplectic geometry, and the introduction of dual mixed variable method into the broad field of applied mechanics, which provides a powerful tool for the discussion of mechanical problems. At the same time, this method, marked by the all state vector, is more in line with and adapts to the development of computer. The trend is very important to the engineering mechanics system, the mathematical physics method and the research of other subjects.