Basic Studies On The Performance Evaluation Theory For Pin-bar Structures Based On Matrix Analysis

The structural health monitoring system of large span space structures is generally designed following the structural design theories at present.Since the traditional design theories only check and calculate the structural performance under the limit state,the established monitoring indicators are not enough to directly and effectively reflect the actual performance of the overall structure.Aiming at the space trusses(such as grids,shells,and etc.)widely used in engineering,a theoretical method that can guide the performance monitoring and design of such existing structures based on matrix analysis is developed in this paper.The related basic research has been carried out focusing on four aspects: the quantitative evaluation of structural geometrical invariance,the efficient calculation of structural redundancy and system reliability,the establishment of structural performance indicators based on stiffness analysis,and the static test of structural key performance.The main contents and innovations of the research in this paper are as follows:(1)The quantitative evaluation method of the geometrical invariance of the pin-bar structures is studied.The least eigenvalue of the state matrix is used to quantitatively characterize the geometrical invariance of the pin-bar structures.The contributions of different elements to the geometrical invariance are evaluated using the projections of the direction vectors of elements on the eigenvector corresponding to the least eigenvalue.Based on the null space basis matrix of the structural equilibrium matrix,two efficient lemmas determining whether the removal(failure)of single or multiple elements will lead to structural geometrical variance are proposed.(2)An efficient method of calculating system reliability for pin-bar structures based on the minimal cut sets is developed.The necessary and sufficient condition for the sub-matrix of the null space basis matrix corresponding to a minimal cut set is proposed and proved.Based on the maximal linearly independent group of the row vectors of the null space basis matrix,a new strategy of determining all the minimal cut sets without omission is proposed,and the structural geometrical stability redundancy is characterized using the minimal dimension of the minimal cut sets.The basic conditions of whether the increase or decrease of elements can cause the change of structural redundancy are studied.It is demonstrated that the system reliability of pin-bar structures depends only on the failure modes consisting of all minimal cut sets and with the largest failure probabilities.(3)The key performance indicators of the structural system stiffness,stability and strength for space trusses are studied oriented to the dominant loads of structural design.The generalized displacement in a direction of the eigenvectors of the elastic stiffness matrix is used to characterize the stiffness contribution of the direction to the displacement induced by the dominant load.The eigenvectors with larger contributions are defined as the key set corresponding to the dominant load,and the corresponding eigenvalues are used to characterize the key stiffness performance of the structural system.The least eigenvalue of the structural tangent stiffness matrix is used as the indicator to quantitatively characterize the system stability performance.A virtual stiffness matrix considering the carrying capabilities reduction of elements is defined,and its least eigenvalue is used as the indicator to quantitatively characterize the key strength performance of the structural system.Considering the time-varying deterioration of the element stiffness,the incremental formulas describing the variation of key performance indicators are derived using the matrix perturbation method,and the variance-based sensitivity analysis method is also proposed.(4)The static test method is developed to monitor the structural key performance.The key set is expanded by including the adjacent eigenvectors,and the displacement of the existing structure is approximately expressed as a linear combination of the eigenvectors in the expanded key set.By constructing several simple loads applied to the existing structure and measuring the displacement responses,the combination coefficient of each eigenvector(pseudo generalized displacement)can be obtained.Then,the displacement of the existing structure under the same dominant load is estimated,and the deterioration of the key performance of the structural system is evaluated indirectly.The strategy for optimizing the magnitudes and layouts of the simple loads is proposed based on matrix analysis,and the efficient independent method is used to determine the selection of measuring degrees of freedom.The deterioration of element stiffness of the existing structure is estimated by measuring the displacement increments between the existing structure and the ideal structure under multiple groups of simple loads,and then the key performance of the system stability and strength is evaluated.