C. V. Girija Vallabhan

A refined model for beams on elastic foundations

Abstract The concept of a beam or slab on an elastic foundation has been one of the convenient tools for obtaining solutions to several geotechnical engineering problems. While it is easy to establish quite accurately the stiffness characteristics of the beam or the slab, the parameters which govern the behavior of the subsoil or the elastic foundation are indeed hard to model. This difficulty remains true even if one assumes that the soil has linear, isotropic, and homogeneous properties. Using the Vlasov model. Vallabhan and Das (1988, J. Engng Mech. Div., ASCE 114 (2). 2072–2082) have developed an effective iterative technique to solve the beam-on-elastic-foundation problem where the soil is assumed to have a uniform depth with a rigid base at the bottom. Geotechnical engineers usually encounter subsoil of finite depth, and normally the elastic properties are considered to remain constant or vary linearly with depth. In this paper, the authors have extended their model to incorporate numerically this physical characteristic of the soil. Even though the derivations may look laborious, the numerical model is quite simple and can be programmed on a desktop computer.

Behaviour of window glass panels during earthquakes

The seismic behaviour of window glass panels is investigated. Glass damage observed in past earthquakes and previous research on the seismic performance of glass components are reviewed. Seismic design code procedures proposed for mitigating the damage sustained by glass components are evaluated. Analytical procedures are developed for calculating the in-plane deformation capacity and out-of-plane resistance of window glass panels subjected to seismic excitation. Simple practical procedures are proposed for the design of glass panels against earthquake effects. These procedures account for the interstorey drift displacements and floor responses of multistorey buildings as well as the mechanical properties of window glass.

A mathematical model for nonlinear stress analysis of sandwich plate units

A mathematical model is developed for the large deflection analysis of sandwich plates that consist of two face plates and an inner core. The face plates can have different thicknesses and they are capable of resisting both membrane and bending forces. The core is compressible due to lateral forces, and capable of resisting transverse shear deformations, but is not capable of resisting bending moments. The mathematical model consists of three nonlinear differential equations.

Experimentally Verified Theoretical Analysis of Thin Glass Plates

Interest in the behavior of window glass under the effects of wind has focused analytical attention on thin glass plates under lateral pressure. While the analysis of thin rectangular glass plates under lateral pressure appeared innocuous, the Committee on Window Glass Research found the solution to be elusive. Several numerical solutions (finite element, finite difference and Galerkin) failed to correlate, at least initially. When theoretical concurrence was achieved, disagreements were found between theoretical and experimental results. Only through carefully exercised theoretical and experimental investigations were good correlations finally accomplished.

Nonlinear dynamic response of window glass plates subjected to fluctuating wind pressures

Abstract It is common practice to analyze and design window glass units using an equivalent static wind pressure. Little is known with regard to the dynamic behavior of window glass units subjected to a fluctuating wind pressure. Here, a mathematical model is developed to determine this dynamic behavior. A random fluctuating wind pressure is simulated using the well known Davenport spectrum for wind velocity and Vaicaitis expression for generating discrete wind velocity-time data. For the analysis of the plate, the dynamic nonlinear von Karman plate equations are used. The dynamic finite difference model developed by Vallabhan and Selvam is modified to consider the response due to sample fluctuating wind pressures. Time dependent displacement and maximum tensile principal stress in two vibrating glass plates are the outcome of this analysis.

Nonlinear dynamic response of window glass units

Abstract For glazing of modern buildings, rectangular window glass units are being used extensively. When these glass units are subjected to lateral wind pressures, they respond dynamically; a simple quasi-static analysis may lead to less conservative design procedures. Since window glass units undergo large displacements when subjected to lateral pressures, a nonlinear dynamic analysis is necessary. Using von Karman nonlinear plate equations, Vallabhan and Selvam (1986) have developed a finite differencemodel for computing the dynamic response of a thin rectangular plate. Here, the maximum amplitudes along with the corresponding periods of vibration and the maximum tensile stresses due to uniform lateral pressures applied suddenly on simply supported thin rectangular plates, are presented using nondimensional parameters. Also, results are presented for various aspect ratios of plates.

A Galerkin model for nonlinear glass plates

Abstract Von Karman plate equations have been found to be satisfactory for the nonlinear stress analysis of thin glass plates. Here a Galerkin approach is used to solve the stress and deflections in a rectangular glass plate used as a window panel using the von Karman equations. The plate is assumed to be simply supported with zero in-plane forces on the boundary. Harmonic functions are used in the Galerkin model. An efficient iterative procedure is employed to obtain the final results.

An efficient solution algorithm for boundary element equations

Abstract Boundary element techniques result in the solution of a linear system of equations of the type HU = GQ + B, which can be transformed into a system of equations of the type AX = F. The coefficient matrix A requires the storage of a full matrix on the computer. This storage requirement, of the order of n * n memory positions ( n = number of equations), for a very large n is often considered negative for the boundary element method. Here, two algorithms are presented where the memory requirements to solve the system are only n * ( n - 1)/2 and n * n /4 respectively. The algorithms do not necessitate any external storage devices nor do they increase the computational efforts.