Optimization of shell structure acoustics

This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large parameter sets in shape optimization problems where the thickness and mid-surface of the shell are computed so as to generate a radiated sound field subject to broad-band design requirements. The structure and acoustics are modeled, respectively, via the Naghdi shell equations, and thin boundary integral equations, with full coupling at the shell mid-surface. In this way, the three-dimensional structural-acoustic equations can be posed as a problem on the two-dimensional mid-surface of the shell. A wide variety of shapes can thus be explored without re-meshing, and the acoustic field can be computed anywhere in the exterior domain with little additional effort. The problem is discretized using triangular MITC shell elements and piecewise-linear Galerkin boundary elements, coupled with a simple one-to-one scheme. Prior optimization work on coupled shell-acoustics problems has been focused on applications with design requirements over a small range of frequencies. These problems are amenable to a number of simplifying assumptions. In particular, it is often assumed that the structure is dense enough that the air pressure loading can be neglected, or that the structural motions can be expanded in a basis of low-frequency eigenmodes. Optimization of this kind can be done with reasonable success using a small number of shape parameters because simple modal analysis permits a reasonable knowledge of the parts of the design that will require modification. None of these assumptions are made in this thesis. By using adjoint equations, derivatives of the radiated field can be efficiently computed with respect to large numbers of shape parameters, allowing a much richer space of shapes, and thus, a broader range of design problems to be considered. The adjoint equation approach developed in this thesis is applied to the computation of optimal mid-surfaces and shell thicknesses, using a large shape parameter set, proportional in size to the number of degrees of freedom in the underlying finite element discretization

A rigorous derivation of second-approximation theory of elastic shells Technical report no. 5

Derivation of second approximation shell theor

Finite element nonlinear transient response analysis of simple 2-d structures subjected to impulse or impact loads

Originally presented as the first author's thesis, (M.S.) in the M.I.T. Dept. of Aeronautics and AstronauticsThis study was intended to contribute to the development of more rational practical methods for predicting the transient responses of structures which are subjected to transient and impact loads. Attention is restricted to the global structural response; local (or stress-wave- induced) response is not included. The use of higher-order assumed- displacement finite elements (FE) is investigated to seek more efficient and accurate strain predictions; these studies were carried out for 2-d structural deformations typical of beams and curved rings to minimize cost and labor. These studies were done in conjunction with the use of various approximations to the nonlinear strain-displacement relations since large deflections and rotations need to be taken into account. Transient large-deflection elastic-plastic structural response predictions are made for these various FE models for impulsively-loaded beams and a free initially-circular ring, for which high quality experimental measurements of strains and deflections are available. From comparisons of (a) predictions with each other for the various FE models investigated and (b) predictions vs. experimental data, it appears to be more efficient for the same number of degree-of-freedom (DOF) unknowns to use the simple 4 DOF/node elements rather than fewer of the more sophisticated 8 DOF/node elements although the latter provide a physically superior and more realistic distribution of strain along the structural span at any given time instant compared with the use of the 4 DOF/N elements. Comparisons of measured with predicted transient strain and final deformation of a thin aluminum beam with both ends clamped and impacted at midspan by a 1-inch diameter steel sphere show very good agreement. Extensions to the present analysis to accommodate more general types of fragments and fragment-impacted structures are discussed briefly