Large natural strains and some special difficulties due to non-linearity and incompressibility in finite elements

The finite element method is now a well established tool for the routine treatment of large linear problems, but the treatment of non-linear problems by the method is yet at the beginning.Section 1 of the present work extends the idea of natural strains and stresses to large strains in simplex finite elements.Section 2 applies some algorithms developed for structural dynamics to the problem of non-linear wave propagation including a case of shock development.Section 3 discusses with numerical examples special difficulties when displacement finite elements are used to solve problems with incompressible or nearly incompressible material.     

Finite element analysis of inelastic structural behaviour

The paper examines computational aspects of the numerical solution of dissipation and diffusion problems which describe inelastic mechanical processes and transport mechanisms of transient environments. Both phenomena are rate processes which lead in general to a system of coupled first order differential equations after finite element idealization of the spatial dependence.     

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

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.     

The natural factor formulation of the stiffness for the matrix displacement method

The natural formulation of the elemental stiffness has proved a most significant interpretation of the elastic behaviour of an element, both from the physical and mathematical point of view. It yields not only concise and elegant matrix expressions for the elements — especially for simplex elements — but leads effortlessly to the non-linear effects associated with large displacements. In the present paper the basic idea is brought to a logical conclusion by the direct construction of the factorised form of the elemental and overall stiffness matrices from their natural stiffness roots. This technique is denoted as the natural factor formulation. It is believed that the new approach leads to a better understanding of the relevant error analysis so powerfully initiated by Rosanoff et al.; see e.g. [20]. The natural factor formulation may also be shown to retain more numerical information of the idealised physical system [21, 28]. Both static and dynamic problems are considered here. For additional information the reader is referred to [16].     

Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems

In the first part of the paper an internal variable model is developed for concrete creep with the following features: creep strain is a linear functional of stress history; application or removal of stress produces instantaneous elastic response; upon removal of stress, creep deformations partially recover, approaching in the limit an irrecoverable part. The mechanism of each creep component is affected be temperature, humidity and loading age.In the second part the internal state variables are derived from concrete creep data with loading ages ranging from 7 to 4560 days and temperatures from 20° to 95°C. Several aging models are examined for which the parameters are determined via least squares optimization. A root mean square criterion is used to assess the approximation.In the third part a step by step algorithm is developed for incremental solution of the time-dependent creep process, noting that the governing equation of evolution lends itself to an economic computer solution without storing previous results. The one-dimensional constitutive statements are extended to multiaxial conditions and subsequently projected from the local level onto the structural level via finite elements (incremental initial load method).In the fourth part the creep behaviour of a prestressed concrete reactor vessel is examined for a loading history which includes hygrothermal effects due to drying and heating as well as prestress and cycling pressure.     

ASKA — Automatic System for Kinematic Analysis A universal system for structural analysis based on the matrix displacement (finite element) method

The system ASKA (Automatic System of Kinematic Analysis) implements the matrix displacement method, using a discretisation technique. Thereby the complete system is idealised into an assembly of finite elements to which a simplified strain pattern is ascribed. The kinematic compatibility conditions are in this procedure satisfied everywhere, but the static compatibility conditions are as a rule only satisfied at the so-called nodal points where the grid-lines of adjoining elements meet. Finally, a system of equations is set up in the degrees of freedom at the nodal points. This method effectively solves a physically idealised system in an as exact a manner as the finite bits operations on the digital computer allow.

Through the years ASKA has been kept up to date by implementing the latest state of the art, be it structural or numerical innovations. For example, the element library, containing about 30 families of elements, certainly represents one of the superior systems today.     

Sustainable energy policy indicators: Review and recommendations

Nowadays, the development of a sustainable indicators’ framework towards the sustainable energy policy making should be characterized by clarity and transparency. Even though the energy policy making has been the subject of many researchers, studies proposing an appropriate framework of sustainable indicators that have to be used are not present in the international literature. The purpose of the current paper is to present an integrated review of the methodologies and the related activities of the energy indicators and to recommend an operational framework of appropriate indicators supporting thus the policy makers/analysts/citizens towards a sustainable energy policy making.