In this work the Bubnov-Galerkin variational method was applied to determine the critical bucklin... more In this work the Bubnov-Galerkin variational method was applied to determine the critical buckling load for the elastic buckling of columns with fixed-pinned ends. Coordinate shape functions for Euler column with fixed-pinned ends are used in the Bubnov-Galerkin variational integral equation to obtain the unknown parameters. One parameter and two parameter shape functions were used. In each case, the Bubnov-Galerkin method reduced the boundary value problem to an algebraic eigen-value problem. The solution of the characteristic homogeneous equations yielded the buckling loads. One parameter coordinate shape function yielded relative error of 4% compared with the exact solution. Two parameter coordinate shape function gave a relative error of 0.77%, which is negligible.
The Stodola-Vianello iteration method was implemented in this work to determine the critical buck... more The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.
In this work the Bubnov-Galerkin variational method was applied to determine the critical bucklin... more In this work the Bubnov-Galerkin variational method was applied to determine the critical buckling load for the elastic buckling of columns with fixed-pinned ends. Coordinate shape functions for Euler column with fixed-pinned ends are used in the Bubnov-Galerkin variational integral equation to obtain the unknown parameters. One parameter and two parameter shape functions were used. In each case, the Bubnov-Galerkin method reduced the boundary value problem to an algebraic eigen-value problem. The solution of the characteristic homogeneous equations yielded the buckling loads. One parameter coordinate shape function yielded relative error of 4% compared with the exact solution. Two parameter coordinate shape function gave a relative error of 0.77%, which is negligible.
The Stodola-Vianello iteration method was implemented in this work to determine the critical buck... more The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.
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