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In this paper the Boundary Element Method (BEM) is developed for the linear buckling analysis of cylindrical shell panels. The present investigation proposes a method based on the concept of the Analog Equation of Katsikadelis. Therefore, the method is referred as the Analog Equation Method (AEM). According to the AEM the three differential equatio...
Citations
... Baiz and Aliabadi using D/BEM in [7] and a boundary-only formulation in [8] presented a solution for the linear buckling problem of shear deformable shallow shells. Present authors used the BEM combined with AEM to develop a boundary-only solution for the linear buckling of general cylindrical shells [9]. ...
... Equations (9) can be directly integrated to yield ...
The meshless analog equation method, a purely mesh-free method, is applied to the buckling analysis
of cylindrical shell panels. The method is based on the principle of the analog equation, which converts the three
governing partial differential equations in terms of displacements into three uncoupled substitute equations,
two Poisson’s equations and one plate equation, under fictitious sources. The fictitious sources are represented
by series of radial basis functions (RBFs) of multiquadric type, and the substitute equations are integrated.
This integration allows the representation of the sought solution by new RBFs, which approximate accurately
not only the displacements but also their derivatives involved in the governing equations. Then, by inserting
the approximate solution in the original differential equations and the associated boundary conditions and
collocating at a predefined set of mesh-free nodal points, a linear algebraic eigenvalue problem results, the
solution of which gives the buckling loads and modes. The optimal value of the shape parameter of the RBFs
is obtained as that minimizing eigenvalues. The method is illustrated by analyzing several shell panels. The
studied examples demonstrate the efficiency and the accuracy of the presented method.
In this work a multi-region boundary element formulation for linear local buckling analysis of assembled plate and shallow shell structures is presented. The assembly is divided into sub-regions. In each sub-region, the formulation is formed by coupling boundary element formulations of shear deformable plate bending and two-dimensional plane stress elasticity. Domain integrals appearing in the formulation (due to the curvature and due to the domain load) are transformed into equivalent boundary integrals. Membrane stresses at discrete domain points of each sub-region (plate or shallow shell) in the assembly are obtained from the prebuckling state, resulting in a set of linear buckling equations in terms of the buckling deflection and the buckling load factor. Buckling equation is presented as a standard eigenvalue problem. Results are compared with FEM solutions and it is shown that good accuracy can be achieved with the present multi-region BEM formulation.
