A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Numerically Stable Solutions to the State Equations for Structural Analyses
The state space method has been widely used to analyze the static and dynamic characteristics of homogeneous, laminated, functionally graded, or even intelligent structures. However, the solution of the state equation using the traditional transfer matrix generally encounters the problem of numerical instability. This work, therefore, derives the general solution to the state equation by making use of similarity transformation to convert the system matrix into a matrix in Jordan canonical form (including the diagonal matrix as a special case), so as to avoid the previously stated problem. A special form of the exponential function is also introduced according to the characteristics of the eigenvalues of the system matrix. Furthermore, the undetermined coefficients in the general solution—rather than the original state variables—are considered as the primary unknowns. Consequently, a new solution with numerical robustness to the state equation is obtained. Finally, numerical examples for the free vibration analyses of beams and plates as well as interfacial shear stress analysis of fiber-reinforced polymer (FRP)-strengthened concrete beams are presented to verify that the proposed procedure can circumvent numerical instability completely.
Numerically Stable Solutions to the State Equations for Structural Analyses
The state space method has been widely used to analyze the static and dynamic characteristics of homogeneous, laminated, functionally graded, or even intelligent structures. However, the solution of the state equation using the traditional transfer matrix generally encounters the problem of numerical instability. This work, therefore, derives the general solution to the state equation by making use of similarity transformation to convert the system matrix into a matrix in Jordan canonical form (including the diagonal matrix as a special case), so as to avoid the previously stated problem. A special form of the exponential function is also introduced according to the characteristics of the eigenvalues of the system matrix. Furthermore, the undetermined coefficients in the general solution—rather than the original state variables—are considered as the primary unknowns. Consequently, a new solution with numerical robustness to the state equation is obtained. Finally, numerical examples for the free vibration analyses of beams and plates as well as interfacial shear stress analysis of fiber-reinforced polymer (FRP)-strengthened concrete beams are presented to verify that the proposed procedure can circumvent numerical instability completely.
Numerically Stable Solutions to the State Equations for Structural Analyses
Xu, Rongqiao (author) / Liu, Xingxi (author) / Jiang, Jiaqing (author) / Wang, Yun (author) / Chen, Weiqiu (author)
2019-12-21
Article (Journal)
Electronic Resource
Unknown
Solving Several Complex Variables Equations Numerically
| British Library Online Contents | 2011
A numerically stable method for convex optimal control problems
| British Library Online Contents | 2004
Numerically stable formulas for a particle-based explicit exponential integrator
| British Library Online Contents | 2015
An Efficient and Numerically Stable Coupled-Mode Solution for Range-Dependent Propagation
| British Library Online Contents | 2012