http://web-static-aws.seas.harvard.edu/hutchinson/papers/evans_multifunc_cellular.pdf

Multifunctionality of cellular metal systems

Essay on uncertainties in elastic and viscoelastic structures: From A. M. Freudenthal's criticisms to modern convex modeling

Thin-walled shell structures like circular cylindrical shells are prone to buckling. Imperfections, which are defined as deviations from perfect shape and perfect loading distributions, can reduce the buckling load drastically compared to that of the perfect shell. Design criteria monographs like NASA-SP 8007 recommend that the buckling load of the perfect shell shall be reduced by using a knock-down factor. The existing knock-down factors are very conservative and do not account for the structural behaviour of composite shells. To determine an improved knock-down factor, several authors consider realistic shapes of shells in numerical simulations using probabilistic methods. Each manufacturing process causes a specific imperfection pattern; hence for this probabilistic approach a large number of test data is needed, which is often not available. Motivated by this lack of data, a new deterministic approach is presented for determining the lower bound of the buckling load of thin-walled cylindrical composite shells, which is derived from phenomenological test data. For the present test series, a single pre-buckle is induced by a radial perturbation load, before the axial displacement controlled loading starts. The deformations are measured using the prototype of a high-speed optical measurement system with a frequency up to 3680 Hz. The observed structural behaviour leads to a new reasonable lower bound of the buckling load. Based on test results, the numerical model is validated and the shell design is optimized by virtual testing. The results of test and numerical analysis indicate that this new approach has the potential to provide an improved and less conservative shell design in order to reduce weight and cost of thin-walled shell structures made from composite material.

Robust design of composite cylindrical shells under axial compression — Simulation and validation

The important role of geometric imperfections on the decrease of the buckling load for thin-walled cylinders had been recognized already by the first authors investigating the theoretical approaches on this topic. However, there are currently no closed-form solutions to take imperfections into account already during the early design phases, forcing the analysts to use lower-bound methods to calculate the required knock-down factors (KDF). Lower-bound methods such as the empirical NASA SP-8007 guideline are commonly used in the aerospace and space industries, while the approaches based on the Reduced Stiffness Method (RSM) have been used mostly in the civil engineering field. Since 1970s a considerable number of experimental and numerical investigations have been conducted to develop new stochastic and deterministic methods for calculating less conservative KDFs. Among the deterministic approaches, the single perturbation load approach (SPLA), proposed by Huhne, will be further investigated for axially compressed fiber composite cylindrical shells and compared with four other methods commonly used to create geometric imperfections: linear buckling mode-shaped, geometric dimples, axisymmetric imperfections and measured geometric imperfections from test articles. The finite element method using static analysis with artificial damping is used to simulate the displacement controlled compression tests up to the post-buckled range of loading. The implementation of each method is explained in details and the different KDFs obtained are compared. The study is part of the European Union (EU) project DESICOS, whose aim is to combine stochastic and deterministic approaches to develop less conservative guidelines for the design of imperfection sensitive structures.

Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells

This report consists of a survey of the state of the art in uncertainty-based design together with recommendations for a Base research activity in this area for the NASA Langley Research Center. This report identifies the needs and opportunities for computational and experimental methods that provide accurate, efficient solutions to nondeterministic multidisciplinary aerospace vehicle design problems. Barriers to the adoption of uncertainty-based design methods are identified. and the benefits of the use of such methods are explained. Particular research needs are listed.

/pdf/needs-and-opportunities-for-uncertainty-based-340lsrnerh.pdf

Needs and Opportunities for Uncertainty-Based Multidisciplinary Design Methods for Aerospace Vehicles

This monograph indicates current practices for predicting buckling of uniform
stiffened and unstiffened circular cylindrical shells under various types of static
loading, and suggests the procedures that yield estimates of static buckling loads considered to be conservative. The buckling of truncated conical shells and shells of double curvature will be treated in separate monographs.

/pdf/buckling-of-thin-walled-circular-cylinders-53m1jhcxkw.pdf

Buckling of Thin-Walled Circular Cylinders

Predicting buckling of thin walled, uniform stiffened and unstiffened circular cylindrical shells under static loading.

V. I. Weingarten

Papers

Buckling of Thin-Walled Circular Cylinders

Buckling of thin-walled circular cylinders, NASA SPACE VEHICLE DESIGN CRITERIA (Structures)