Hans-Peter Mlejnek

An engineer's approach to optimal material distribution and shape finding

Abstract The fundamental aim of shape optimization involves the optimal distribution of mass in space observing global and local design constraints. The practical realization in applied mechanics can be performed by introducing a foam like material, with variable density as discussed by Bendsoe and Kikuchi. This paper uses for the evaluation of material properties a simple energy approach. The application is extended to three-dimensional domains. Multiple loading cases are also considered. Further, the approach is implemented in a preoptimizer for optimal shape finding.

On an unconventional but natural formation of a stiffness matrix

Abstract The paper describes a procedure of deriving stiffness matrices for finite elements based on the patch-test using the natural method. The latter is found once more to greatly simplify the formulation and to result in compact natural stiffness matrices. The procedure is tested on the construction of a triangular plate-bending element TRUNC, the natural stiffness of which appears as a simple hyperdiagonal matrix. Sample problems using the TRUNC element show that the element converges quickly and is therefore well suited for engineering purposes.

Computational prediction and redesign for viscoelastically damped structures

Abstract Viscoelastic materials are very effective in suppressing excessive vibrations and noise. The shear modulus of these materials has an important effect on the loss factors of damped structures. However, it changes rapidly with frequency, an effect, which has to be taken into account. This paper presents a method, namely the finite element perturbation method, which provides a simple tool for the prediction in a wide frequency range without repeated analysis. This approach also enables a simplified redesign of damping.

Some considerations on the natural approach

Abstract In this note we present some pertinent comments on the natural mode technique. In the first part we demonstrate that for arbitrary finite elements the choice of urelements may exclusively be based on simplex elements. In fact, the corresponding infinitesimal building blocks, the so-called subelements, may be used also for quadrilateral and hexahedronal elements or for that matter for any one-, two- or three-dimensional element. The second part develops some new considerations on unconventional models associated with the patch test.

On the natural factor in nonlinear analysis

Abstract The natural factor approach as formulated for the linear displacement method is extended to nonlinear analysis. It is shown that the sparse population of the matrix factor may be efficiently utilized in the decomposition technique. Furthermore, it is demonstrated that in ill-conditioned cases the method performs numerically better than the standard Cholesky approach.

A new iterative solution for structures and continua with very stiff or rigid parts

Abstract Structures with widely different orders of stiffness or nearly incompressible continua are not uncommon in structural analysis and give considerable computational difficulties when using the matrix displacement method on a 32 or 36 bit word computer. This paper presents three approaches to overcome these problems. The first one is based on the idea of the natural method. The second one makes exclusively use of the widely used cartesian notation. Finally the third one considers structures with only a few rigid members. One central aim of this paper is to implement the developed theoretical tools in standard finite element packages. The paper has illustrative hand and computer solutions and the appendix presents the underlying rigorous mathematical proofs.

Some Approaches for Shape Finding in Optimal Structural Design

Shape optimization by moving boundaries is now a well established technology, which enters commercial programs. Following the philosophy of Schmit [1], Fleury [2] and many other contributions, the movable shape problem is described by means of a blending function, which is governed by a comparatively small number of variables. This property disposes the approach favourable to mathematical progamming (MP), which can handle all types of objectives and constraints very easily. However since we have to preselect the position of the moving boundary as well as the type of the blending function, the process of finding an optimal shape is quite predetermined. We are for instance not able to create automatically voids.

On accurate stress calculation in static and dynamic problems using the natural factor approach

Abstract The natural factor approach was introduced during the last few years as a tool for more accurate computations of displacements [1]. This paper presents an economic iterative procedure for the precise determination of stresses in numerically critical large scale problems. In addition, it furnishes a corresponding error analysis. Furthermore, we discuss the stress (and displacement) computations for unsupported structures under self-equilibrating loads as they may arise in dynamic analysis. Finally, some examples are given.

THE NATURAL METHOD: SIMPLE AND ELEGANT

The paper presents a survey of the natural mode technique with special emphasis on plate and shell type structures. First, the natural method is briefly recapitulated on the basis of the plane triangular simplex element (TRIM3). Such an element with its simple natural deformation modes (elongations of the sides) may then be used in a differential sense as building block for higher order and curved membrane elements which are not necessarily of triangular shape. This is the basic idea of the subelement concept.

Ein Abriß der Aeroelastizität

Wir sind nun beim letzten Kapitel des dritten und abschliesenden Bandes dieses Werkes angelangt. Nachdem wir uber 35 Jahre hinweg das Studium der Luft- und Raumfahrttechnik an zwei Universitaten aufgebaut haben, betrachten wir es als eine konsequente Pflichtubung, aber auch als einen sentimentalen Epilog, in diesem letzten Kapitel auf ein ausgesprochen luftfahrtspezifisches Gebiet, das des Flatterns, einzugehen. Flattern stellt ein eigenartiges Phanomen des Zusammenwirkens der nichtkonservativen Luftkrafte mit der elastischen Struktur dar, das sowohl in statischer wie in dynamischer Hinsicht wirksam werden und im Grenzfall zu einer Katastrophe fur das Flugzeug fuhren kann. In vorliegender Darstellung werden wir die aerodynamischen Krafte, die wieder in Matrizenform angeordnet werden, als gegeben ansehen mussen, da unser Werk hauptsachlich auf die Struktur ausgerichtet ist.