The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral...The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.展开更多
The present study aims to develop a robust structural damage identification method that can be used for the evaluation of bridge structures. An approach for the structural damage identification based on the measuremen...The present study aims to develop a robust structural damage identification method that can be used for the evaluation of bridge structures. An approach for the structural damage identification based on the measurement of natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. A computational procedure for the direct iteration technique based on the non-linear perturbation theory is proposed to identify structural damage. The presented damage identification technique is applied to the footbridge over the Slunjcica River near Slunj to demonstrate the effectiveness of the proposed approach. Using a limited number of measured natural frequencies, reduction in the stiffness of up to 100% at multiple sites is detected. The results indicate that the proposed approach can be successful in not only predicting the location of damage but also in determining the extent of structural damage.展开更多
For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorho...For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorhombic crystal systems. Transformations have been done in this paper and the general compliance transformation relations from the orthogonal coordinate systems (Yi) to the measurement systems (Mi) are given for all seven crystal systems. Accordingly, useful expressions for Young's modulus E and Poisson's ratio are also derived.展开更多
基金Sponsored by the National Key Technology Research and Development Program (Grant No.2006BAJ12B03-2)
文摘The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.
文摘The present study aims to develop a robust structural damage identification method that can be used for the evaluation of bridge structures. An approach for the structural damage identification based on the measurement of natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. A computational procedure for the direct iteration technique based on the non-linear perturbation theory is proposed to identify structural damage. The presented damage identification technique is applied to the footbridge over the Slunjcica River near Slunj to demonstrate the effectiveness of the proposed approach. Using a limited number of measured natural frequencies, reduction in the stiffness of up to 100% at multiple sites is detected. The results indicate that the proposed approach can be successful in not only predicting the location of damage but also in determining the extent of structural damage.
文摘For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorhombic crystal systems. Transformations have been done in this paper and the general compliance transformation relations from the orthogonal coordinate systems (Yi) to the measurement systems (Mi) are given for all seven crystal systems. Accordingly, useful expressions for Young's modulus E and Poisson's ratio are also derived.
