Analysis of elastic systems with discontinuous parameters
Constructions in the form of rectangular planar plates and shallow shells reinforced by a cross system of ribs of great rigidity and loaded with an arbitrary lateral load are considered. The stress-strain state of such structures is described by technical theories of plates and shallow shells. The effect of the stiffeners is taken into account in the equations as additional terms containing factors with the Dirac δ-function and its derivatives. The plate and the shell may have a stepwise variable thickness. The ribs are arbitrary thin-walled beams of variable cross-section that play an essential role in providing the load-carrying capacity of the structure as a whole. The stress-strain state of not only the plate and the shell but also the stiffeners themselves is determined. The questions of the rate of convergence of solutions in the form of trigonometric series describing the stress-strain state in the stiffeners are discussed. The results of analyses of reinforced plates are presented.
Calculation of the ribbed plate in the mixed form “deflection - function of efforts”
Analytical solution of a boundary-value problem for a system of differential equations of deformation is obtained for the rectangular plate supported with ribs of rigidity in the “function of deflection - function of efforts” mixed form. The solution is presented in the form of a series over combinations of regular and special discontinuous functions. The solution leads to fast converging series. A simple algorithm for computations is provided.
Evaluation of buckling load and dynamic performance of steel shear wall retrofitted with strips made of shape memory alloy
One of the most imperfections of the steel shear wall is out of plane displacements that cause severe damage in both structural and non-structural elements. In this paper, the effects of shape-memory alloys on steel shear walls are investigated. First, a numerical analysis using the finite element method in ABAQUS software has been carried out according to an experimental test. The results of the numerical analysis have been verified with experimental results. Next, shape-memory alloy fibers have been added vertically and horizontally to various parts of the steel shear wall. The results show that retrofitting with the shape-memory alloy reduces the out-of-plane displacement of the steel shear wall under both cyclic and seismic loadings. Besides, the buckling load in the steel shear wall increases when it is retrofitted with the shape-memory alloy. Also, the total out-of-plane movement (accumulated absolute displacements) of the steel shear wall and non-structural damage are controlled by the characteristic of a shape-memory alloy material called “super-elastic”.