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Papers by Srinivas Gopal Krishna

International Journal of Solids and Structures, Nov 1, 2007

The physical parameters of optimal discrete link-spring models, which maximize the buckling load,... more The physical parameters of optimal discrete link-spring models, which maximize the buckling load, are reconstructed. The cases where the system is pinned or clamped at one end, and supported by linear spring at the other end, are analyzed. It is shown that the optimal system can be determined recursively by using a one parameter iterative loop. For the pinned-spring-supported boundary

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Dec 1, 2008

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009

This article deals with the problem of maximizing the lowest eigenvalue of an affine sum of symme... more This article deals with the problem of maximizing the lowest eigenvalue of an affine sum of symmetric matrices subject to a constraint. It is shown that by the repeated use of eliminants, the problem may be reduced in a systematic manner to that of finding the roots of certain polynomials. However, the process of finding the analytical solution is tedious. Therefore, a Newton iterative method, which solves the problem numerically, is developed. To demonstrate the results, the Lagrange problem of determining the shape of the strongest column is formulated in the discrete model setting and solved by using the developed method. The design problem of finding the mass distribution in a vibratory system that optimizes its extreme natural frequencies is also given.

American Journal of Physics, 2011

Linear perturbation analysis is used to determine the natural frequency of two pendulums connecte... more Linear perturbation analysis is used to determine the natural frequency of two pendulums connected by a rod. The analysis indicates a zone of instability in what looks like a stable system. The paradoxical phenomenon is explained, and a simple experiment confirms the instability.

Optimization techniques and numerical methods were developed to arrive at the shape of the strong... more Optimization techniques and numerical methods were developed to arrive at the shape of the strongest clamped-free and pinned-pinned column. Unimodal solutions of the Lagrange problem were also obtained for the special case where minimum area constraints were given. A mathematical model for columns on elastic foundation also was derived and transformed to an affine sum problem. Unimodal solution of shape of the strongest pinned-pinned column on an elastic foundation was obtained. In addition the application in vibration and buckling, it is believed that the optimization principles and numerical methods developed in this research will be applicable in other fields such as optimal control. x

Volume 3: Design; Tribology; Education, 2008

Columns are main structural members that carry axial loads, which can be combined with bending an... more Columns are main structural members that carry axial loads, which can be combined with bending and shear loads. Unlike most load-carrying members slender columns fail due to buckling rather that yielding, as the bucking load is lesser than that required for yielding. The governing differential equation of buckling when an Euler-Bernoulli beam-column carries an axial load P, depends on the geometry (moment of inertia) I , the elastic modulus E of the column and boundary conditions. This fourth-order Sturm-Louiville differential equation is given by

International Journal of Solids and Structures, Nov 1, 2007

The physical parameters of optimal discrete link-spring models, which maximize the buckling load,... more The physical parameters of optimal discrete link-spring models, which maximize the buckling load, are reconstructed. The cases where the system is pinned or clamped at one end, and supported by linear spring at the other end, are analyzed. It is shown that the optimal system can be determined recursively by using a one parameter iterative loop. For the pinned-spring-supported boundary

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Dec 1, 2008

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009

This article deals with the problem of maximizing the lowest eigenvalue of an affine sum of symme... more This article deals with the problem of maximizing the lowest eigenvalue of an affine sum of symmetric matrices subject to a constraint. It is shown that by the repeated use of eliminants, the problem may be reduced in a systematic manner to that of finding the roots of certain polynomials. However, the process of finding the analytical solution is tedious. Therefore, a Newton iterative method, which solves the problem numerically, is developed. To demonstrate the results, the Lagrange problem of determining the shape of the strongest column is formulated in the discrete model setting and solved by using the developed method. The design problem of finding the mass distribution in a vibratory system that optimizes its extreme natural frequencies is also given.

American Journal of Physics, 2011

Linear perturbation analysis is used to determine the natural frequency of two pendulums connecte... more Linear perturbation analysis is used to determine the natural frequency of two pendulums connected by a rod. The analysis indicates a zone of instability in what looks like a stable system. The paradoxical phenomenon is explained, and a simple experiment confirms the instability.

Optimization techniques and numerical methods were developed to arrive at the shape of the strong... more Optimization techniques and numerical methods were developed to arrive at the shape of the strongest clamped-free and pinned-pinned column. Unimodal solutions of the Lagrange problem were also obtained for the special case where minimum area constraints were given. A mathematical model for columns on elastic foundation also was derived and transformed to an affine sum problem. Unimodal solution of shape of the strongest pinned-pinned column on an elastic foundation was obtained. In addition the application in vibration and buckling, it is believed that the optimization principles and numerical methods developed in this research will be applicable in other fields such as optimal control. x

Volume 3: Design; Tribology; Education, 2008

Columns are main structural members that carry axial loads, which can be combined with bending an... more Columns are main structural members that carry axial loads, which can be combined with bending and shear loads. Unlike most load-carrying members slender columns fail due to buckling rather that yielding, as the bucking load is lesser than that required for yielding. The governing differential equation of buckling when an Euler-Bernoulli beam-column carries an axial load P, depends on the geometry (moment of inertia) I , the elastic modulus E of the column and boundary conditions. This fourth-order Sturm-Louiville differential equation is given by