Robustness Analysis and Important Element Evaluation Method of Truss Structures

This article examines the application of the theory of critical strain energy levels to the determination of the limiting states of rod systems. A redundant truss is chosen to illustrate the peculiarities of changes in the self-stressing states of the structure at critical strain energy levels. The removal of ties when they reach their stress or strain limits leads to a change in the state of self-stress in the structure, which is illustrated by the removal of the rods in the trusses. The matrix notation of the governing equations for the structure allows us to visualize both the formulation of the problem and the course of its solution. We present the formulation and algorithm for solving the problem of a weak link in the structure by the example of a five-core redundant truss. The basic equations of matrix structural mechanics are given, allowing us to implement the algorithm and to determine the unknown parameters of the problem in the form of the method of displacements and the method of forces. The mathematical model of the problem is presented in the form of an eigenvalues problem, which allows us to investigate the extreme properties of the structure’s strain energy in the whole area of admissible parameter values, including the boundaries. The eigenvalues and eigenvectors make it possible to determine the extreme values of the nodal reactive forces of the structure or displacements, depending on the chosen formulation of the problem. The internal forces and deformations in the rods depend on the nodal vectors of external influences. The applied design load is balanced by the internal forces of the system and remains unchanged. This follows from the equality of the work of external forces to a part of the potential energy of the structure. The remaining part of the strain energy allows us to find the limit values of the reactive response of the structure to external actions. Additional actions on the structure can lead to the bearing capacity lost if they exceed the limits of the structure’s response. Examples show an algorithm for finding the weak link in a structure and identifying the rods that will be the first to fail under external loads. The matrices of stiffness and flexibility are formed, and the eigenvalues and vectors are found, which allow for the construction of the limit surface of allowable influences on the structure.

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“…There are optimizations and other methods for evaluating trusses' internal forces presented in [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Implementation of the Weak Link Problem for Trusses

Stupishin

Mondrus

2023

Buildings

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“…Zhou [12] defined the node displacement response change after the initial failure as the object of sensitivity analysis to calculate the importance coefficient of the element. According to the sensitivity analysis, the structure robustness is evaluated by the change of structural strain energy after element failure, and the element importance is inversely proportional to the robustness coefficient, performed by Feng et al [13]. Zhang et al [14] obtained the maximum load coefficient from the load-deflection curve.…”

Section: Introductionmentioning

confidence: 99%

Application of Sensitivity Analysis to Progressive Collapse Resistance of Planar Truss Structures

Ke¹,

Liu²

2022

Applied Sciences

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The conventional sensitivity analysis method unanimously takes all remaining elements except the damaged ones as statistical objects, and element importance is evaluated by the mean value of the sensitive indices of statistical objects. However, from the perspective of resisting progressive collapse, the method is not sufficiently targeted, and the evaluation results have some mistakes. The shortcomings of the traditional sensitivity analysis method in element importance evaluation were analyzed and compared through finite element investigations of two types of planar trusses. Based on the anti-progressive collapse mechanism of the planar truss, the sensitivity analysis method with lower chords as statistical objects was proposed to evaluate the importance of planar truss structural elements. This method is conceptually straightforward, and the assessment results are beyond-compare regarding accuracy via comparison against the results of other evaluation methods. Furthermore, based on identifying important elements, the structure’s bearing capacity can be improved by targeted anti-progressive collapse design.

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“…Over recent decades, with the sudden increase of accidents and terrorist activities, some progressive collapse accidents have occurred, causing serious casualties, property losses, and social impacts [1][2][3][4]. The safety of the structure has drawn paramount attention.…”

Section: Introductionmentioning

confidence: 99%

Applications of Energy-Based Evaluation Method of Element Importance to Grid Structures

Wang

Feng

et al. 2022

Symmetry

Self Cite

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It is necessary to perform the robustness design for the progressive collapse resistance of grid structures. However, there is a lack of a comprehensive index to evaluate the member importance. An evaluation method on element importances is proposed based on the element strain energy and element removal technology. The element importance coefficients can be calculated based on the change of strain energy vectors after the removal of analyzed elements using ANSYS. The influence of the loading pattern, boundary condition, and geometric parameters of square pyramid grid structures are investigated. Moreover, the other three types of spatial grids are introduced to explore the difference in element importance distributions. The considerable difference in element importance coefficient distribution for different grid structures shows that it is essential to establish a general program for rapid model robustness analysis. This principle in this work can be easily integrated into the existing design and analysis platform to make up for this shortcoming.

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Robustness Analysis and Important Element Evaluation Method of Truss Structures

Cited by 6 publications

References 35 publications

Implementation of the Weak Link Problem for Trusses

Implementation of the Weak Link Problem for Trusses

Application of Sensitivity Analysis to Progressive Collapse Resistance of Planar Truss Structures

Applications of Energy-Based Evaluation Method of Element Importance to Grid Structures

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