Theory of matrix structural analysis

Finite element modelling of distribution problems

A simple finite element model for the warping torsion problem

Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.

Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle

A monotonicity analysis theory for the dependent eigenvalues of the vibrating systems

Aircraft fuselages are inevitably weakened by a large number of cutouts. In particular large cut-outs in the pressure cabin, like those for doors, remain highly fatigue sensitive. This is not only due to the fact that the cut-out causes a large stress concentration, but is also due to the use of the door in service. This considerably increases the chance of accidental damage. It is obvious, therefore, that the reinforcement around a cut-out must be designed with care. The large number of repair patches around doors and other large cut-outs, found on virtually all aircraft over a certain age, clearly shows that the currently used design methods are inadequate. An improved design method for cut-outs in pressurized aircraft fuselages is described in this thesis. The design aspect should be emphasized, because design is more than simply the availability of an appropriate analysis method. A design procedure must by definition include the sizing of the structure and, moreover, must provide the designer with sufficient information to understand its behaviour. The latter aspect is especially important, because this allows the designer to concentrate on the creative part of the design task. Reduction of the time taken in design is obviously important from an economical point of view. Besides economic advantages, reduction of the time taken in design is also important with respect to changes in design. A door together with its surrounding structure, is often redesigned to meet individual customer requirements and this redesign often has to be performed in a very short time. The design method presented in this thesis offers a procedure for the prediction and modification of the stresses around a cut-out by means of finite element analysis, optimization, sensitivity studies and "what-if' analysis. The design tool developed speeds up the design process by around an order of magnitude. The design method is applied to an existing aircraft and the results compared to experimental data. A parameter study is performed to identify the most effective members of the reinforcing structure.

Theory of matrix structural analysis

Citations

Finite element modelling of distribution problems

A simple finite element model for the warping torsion problem

Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle

A monotonicity analysis theory for the dependent eigenvalues of the vibrating systems

Design of cut-outs in shell structures

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