http://milad-engc.persiangig.com/Recent.pdf

Recent research advances on the dynamic analysis of composite shells: 2000-2009

A review of topology optimization for additive manufacturing: Status and challenges

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

A model to predict low-velocity impact response and damage in sandwich composites

Investigations on imperfection sensitivity and deduction of improved knock-down factors for unstiffened CFRP cylindrical shells

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 discrepancy between the analytically determined buckling load of perfect cylindrical shells and experimental test results is traced back to imperfections. The most frequently used guideline for design of cylindrical shells, NASA SP-8007, proposes a deterministic calculation of a knockdown factor with respect to the ratio of radius and wall thickness, which turned out to be very conservative in numerous cases and which is not intended for composite shells. In order to determine a lower bound for the buckling load of an arbitrary type of shell, probabilistic design methods have been developed. Measured imperfection patterns are described using double Fourier series, whereas the Fourier coefficients characterize the scattering of geometry. In this paper, probabilistic analyses of buckling loads are performed regarding Fourier coefficients as random variables. A nonlinear finite element model is used to determine buckling loads, and Monte Carlo simulations are executed. The probabilistic approach is used for a set of six similarly manufactured composite shells. The results indicate that not only geometric but also nontraditional imperfections like loading imperfections have to be considered for obtaining a reliable lower limit of the buckling load. Finally, further Monte Carlo simulations are executed including traditional as well as loading imperfections, and lower bounds of buckling loads are obtained, which are less conservative than NASA SP-8007.

Probabilistic design of axially compressed composite cylinders with geometric and loading imperfections

Rapid simulation of impacts on composite sandwich panels inducing barely visible damage

Aerospace industry demands for significantly reduced development and operating costs. Reduction of structural weight at safe design is one avenue to achieve this objective. The running ESA (European Space Agency) study Probabilistic Aspects of Buckling Knock Down Factor acts on this route. It concentrates on thin-walled circular cylindrical CFRP shells subjected to axial compression. It is well known that such structures exhibit not only a high load carrying capacity but also are prone to buckling which is highly imperfection sensitive. Imperfections are defined as deviations from perfect parameters like shape, thickness, material properties and loading distributions, they can reduce the buckling load drastically compared to a perfect shell. In order to account for these imperfections the theoretical buckling load of a perfect cylinder must be multiplied, and therefore reduced, by a knock-down factor (the ratio of buckling loads of imperfect and perfect cylindrical shell). Thus the closer the knock-down factor reflects the effect of imperfections the better is the prediction of the real buckling load.
In the still used NASA SP-8007 design guideline from 1968 a lower bound curve for the knock-down factor is proposed. The factor depends on the slenderness (the ratio of radius and wall thickness) and decreases with increasing slenderness. This factor is rather conservative and the structural behaviour of composite material is not considered adequately. Advanced thin-walled cylindrical shell structures under compression are therefore penalized if the knock-down factor based on this early NASA report must be applied.
The current ESA study started in May 2006 and will run for 18 months. Its main objective is to achieve a better buckling knock-down factor for unstiffened CFRP cylindrical shells and to validate the linear and non-linear buckling simulations by test results. The main results will comprise an experimental data base (material properties, measured thicknesses, full scale shape imperfections, load-shortening curves, strains, and deformations) obtained by testing of 10 nominally identical axially compressed CFRP cylindrical shells, sensitivity analyses using Monte-Carlo simulation, validation with tests and a design guideline for that type of structure with a less conservative knock-down factor than taken from NASA SP-8007. All tasks of the ESA study are performed at the Institute of Composite Structures and Adaptive Systems of DLR Braunschweig, which has a rich body of experience in design, manufacturing, testing and analysis of shells prone to buckling.
The paper outlines the objectives and expected results of the running ESA study and presents the results achieved so far.

Probabilistic approach for improved buckling knock-down factors of CFRP cylindrical shells

A new four-node bilinear shell element with full piezoelectric coupling is presented. It can be used for the analysis of light-weight smart structures (adaptive structures), i.e. laminated composite structures with piezoelectric patches attached to its surface or embedded within the laminated layers. The piezoelectric patches can be both passive (sensors) or active (actuators). The element has been successfully integrated into ANSYS 7.1 and thus can take full advantage of all capabilities of this commercial package, e.g. the connection to electric circuit elements, so far within the scope of linear problems.
The element is a continuum-based degenerated solid shell element based on the Reissner-Mindlin theory of plates. It uses the modification of the enhanced assumed strain (EAS) theory for the in-plane strains together with the discrete shear gap method for the transverse shear strains, hence it is free of both membrane locking and shear-locking in bending. It has six mechanical degrees of freedom at each node without difficulties in the drilling rotations, and up to six voltage degrees of freedom. A special logic has been implemented so as to allow for a natural description of the electric interconnections between the piezoelectric layers.
The element passes the structural patch tests from the standard set of tests proposed by MacNeal and Harder (Finite Element Anal. Design 1985; 1:3-20) including warped geometry problems. The piezoelectric behaviour was verified by comparing it with analytical solutions for plannar and curved geometry. A further validation was made by comparison with experimental measurements of harmonic response of actuated beam having both active and passive piezoelectric patches. A good agreement of the results was achieved. It can be concluded that the combination of the theories used makes this element robust and reliable. Copyright © 2006 John Wiley & Sons, Ltd.

Jan Teßmer

Papers

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

Probabilistic design of axially compressed composite cylinders with geometric and loading imperfections

Rapid simulation of impacts on composite sandwich panels inducing barely visible damage

Probabilistic approach for improved buckling knock-down factors of CFRP cylindrical shells

High-performance four-node shell element with piezoelectric coupling for the analysis of smart laminated structures