Abstract

A proposal to estimate both the hydrodynamic pressures and the maximum wave height of liquids contained in rectangular tanks subjected to earthquake ground motions is presented. The computation procedure, based on the Rayleigh-Ritz method, assumes the fluid as a continuum and it does not use concentrated masses or springs. The solution is achieved by equating the seismic input energy of the system with the total kinetic energy of the fluid assuming liquid velocity fields. The resulting design formulas are simple and they are intended to simplify the seismic design of tanks. Numerical results lead to both the liquid maximum sloshing height and hydrodynamic pressure distributions that are similar to those obtained with other simplified methods and those estimated with the finite element method. Preliminary estimations of shear forces and bending moments for a numerical example resulted 13% and 6% larger (respectively) than the corresponding values obtained with the finite element method.

Abstract

During the last 20 years computational progress has significantly increased the capacity to determine the behavior of structures under complex loading conditions through finite element models analysis. This computational power can be used to build complex detailed finite element models but also to resolve more complex equations which were not possible to be coded before. Accurate buckling prediction is still a key factor on optimized structural designs. The accurate determination of the onset of buckling is absolutely essential to determine the initial point of instability and the subsequent post-buckling capability. Determining if the buckling will lead to immediate failure or the loading will be able to be redistributed afterwards is a major point to be considered. Designing a structural component with loading redistribution capability optimize the weight and increase the accuracy, so is a key objective of designers on structural components like torque boxes or fuselage skin. During years Airbus has been focused on developing accurate buckling predictions from close form solutions to complex energy methods development. This paper aims to summarize the evolution of such methods with special emphasis in energy methods and the best practices followed in Airbus for development. On top a summary of potential room for improvement and further evolution will be proposed.

Abstract

This work presents a semi-analytical approach to calculate rapidly but accurately the buckling onset of metallic and composite circular cylindrical shells with various boundary conditions under in-plane and/or pressure loads by the Rayleigh-Ritz method. Results are compared with analytical solutions and detailed finite element models reported in the literature. The proposed approach allows a quick buckling analysis of circular cylindrical shells, which makes it an ideal candidate to be used as part of an optimization scheme and/or to reduce potentially the number of detailed finite element models employed in the early design phases.

Abstract

The stability of composite material plates is being developed following basically two procedures: finite element analysis (FEA) and mathematical approaches using the energy method. The advantage of the finite element models is that they can be used with any geometry, configuration and load combination. However, it requires a significant pre-processing, computation and post-processing time of the results. On the other hand, analytical methods require much less time to obtain the results compared to them, but are limited to just basic geometries, such as rectangular panels without lightening holes. In this work, an analytical approach based on the energy method for buckling analysis of composite panels with holes has been developed. The innovation of this method is the inclusion of holes with different shapes in any position of a trapezoidal panel submitted to any in-plane loads combination. An exhaustive validation has been performed using FEA models and test results.