Abstract
The computationally efficient damage identification technique for truss structures with elastic supports is proposed based on the force method. To transform the truss with supports into the equivalent free-standing model without supports, the novel zero-length dummy members are employed. General equilibrium equations and kinematic relations, in which the reaction forces and the displacements at the elastic supports are taken into account, are clearly formulated. The compatibility equations, in terms of forces in which the flexibilities of elastic supports are considered, are explicitly presented using the singular value decomposition (SVD) technique. Both member and reaction forces are simultaneously and directly obtained. Then, all nodal displacements including constrained nodes are back calculated from the member and reaction forces. Next, the microgenetic algorithm (MGA) is used to properly identify the site and the extent of multiple damages in truss structures. In order to verify the superiority of the current study, the numerical solutions are presented for the planar and space truss models with and without elastic supports. The numerical results indicate that the computational effort required by this study is found to be significantly lower than that of the displacement method.
Highlights
The development of methods with higher computation efficiency is a crucial subject in engineering problems, and elimination of undue repetition in the analysis and the design procedures can lead to a considerable reduction in computation efficiency
The displacement method has been considered as a dominated structural analysis method due to its generality and simplicity in the computer implementation, and a lot of commercial softwares have been developed based on this method
In comparison with the displacement method, the force method has its own advantages: (a) generating accurate stress and displacement results even for modest finite element models, since both equilibrium and compatibility conditions are simultaneously satisfied; (b) the properties of members of a structure most often depend on the member forces rather than the joint displacements; (c) simple formulation for optimization problems including stress constraints; and (d) easier basic concept
Summary
The development of methods with higher computation efficiency is a crucial subject in engineering problems, and elimination of undue repetition in the analysis and the design procedures can lead to a considerable reduction in computation efficiency. In comparison with the displacement method, the force method has its own advantages: (a) generating accurate stress and displacement results even for modest finite element models, since both equilibrium and compatibility conditions are simultaneously satisfied; (b) the properties of members of a structure most often depend on the member forces rather than the joint displacements; (c) simple formulation for optimization problems including stress constraints; and (d) easier basic concept. A computationally efficient numerical procedure is proposed for the damage detection of the truss structures accounting for the flexibilities of the elastic supports through the force method. The numerical solutions are presented for the planar and space truss models in order to show the superiority of the proposed methodology
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