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The study of vibrations of shells is an important aspect in the design of thin-walled structures. In general, analytical solutions for the natural frequencies of shells are not possible, and computational techniques are required. In this paper, modal analysis of shallow shells using a new boundary element method formulation is presented. The proposed formulation is based on a direct time-domain integration using the elastostatic fundamental solutions for both in-plane elasticity and shear-deformable plates. We modeled shallow shells by coupling the boundary element formulation of a shear-deformable plate and the two-dimensional plane stress elasticity. Effects of shear deformation and rotatory inertia were included in the formulation. Domain integrals related to inertial terms were treated by the dual reciprocity boundary element method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation. [ABSTRACT FROM AUTHOR]

Dynamic plate bending problems appear on civil, mechanical, aerospatial and naval applications. The complexity involved in the dynamic response of plates brings many challenges from a mathematical standpoint. In this work, the transient dynamic analysis of elastic shallow shells under uniformly distributed pressure loads, using a dual reciprocity boundary element formulation, is presented. A boundary element formulation based on a direct time-domain formulation using elastostatic fundamental solutions was used. Effects of shear deformation and rotatory inertia were included in the formulation. Shallow shells are modeled coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Domain integrals related to inertial terms were treated using the Dual Reciprocity Boundary Element Method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation. [ABSTRACT FROM AUTHOR]

Highlights: [•] Modal and harmonic Boundary Element Method analysis of elastic shallow shells is presented. [•] A direct time-domain formulation using elastostatic fundamental solutions is proposed. [•] Effects of shear deformation and rotatory inertia were included in the formulation. [•] Integrals related to inertial terms were treated using the Dual Reciprocity Boundary Method. [•] Results show good agreement with those obtained from finite element models. [ABSTRACT FROM AUTHOR]