Numerical analysis of a generalized plane elastica

This article presents the derivation of a very straightforward approximate procedure for the analysis of a continuous flexible member. Since very large deformations are anticipated, a shooting method is utilized along with Newton-type iteration for improved estimates. The resulting computer program is used to compare with exact solutions for a new examples.     

Note on the ‘Alpha’-constant stiffness method for the analysis of non-linear problems

A procedure for the acceleration of convergence in non-linear analysis using the modified Newton–Raphson problem is described. The process has been found useful in plasticity and large deformation studies and its application elsewhere can be envisaged.     

Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

Technological forming processes of thermo-elastoviscoplastic solids are numerically simulated via finite elements based on an appropriate theoretical framework. Departing from the local balance laws of linear momentum and internal energy, the constitutive behaviour is introduced via the concept of ‘generalized standard materials (gsm)’, where a thermodynamic potential and a dissipation potential are the only two scalar quantities needed. They are expressed in invariants of symmetric mixed-variant tensors, respectively. Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used. The numerical solution (of the non-linear coupled thermomechanical problem) is carried out via ‘displacement and assumed enhanced displacement-gradient’-based finite ring-elements in an ‘isentropic’ mechanical phase and via ‘temperature’-based finite ring-elements in an isogeometrical thermal phase and a global Newton–Raphson iterative method in both phases, respectively. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given. © 1998 John Wiley & Sons, Ltd.     

A simple approximate expression for finite life fatigue behaviour in the presence of ‘crack‐like’ or ‘blunt’ notches

In this note, we explore the possibility of simple extensions of the heuristic El Haddad formula for finite life, as an approximate expression valid for crack‐like notches, and of the ‘Luká? and Klesnil’ equation for blunt notches. The key starting point is to assume, in analogy to the Basquin power‐law SN curve for the fatigue life of the uncracked (plain) specimen, a power law for the ‘finite life’intrinsic El Haddad crack size. The approach has similarities with what recently proposed by Susmel and Taylor as a Critical Distance Method for Medium‐Cycle Fatigue regime. Reasonable agreement is found with the fatigue data of Susmel and Taylor for notches, and in particular the error seems smaller in finite life than for infinite life, where these equations are already used. In these respects, the present proposal can be considered as a simple empirical unified approach for rapid assessment of the notch effect under finite life.     

‘Infinite domain’ elements

A parametric element is formulated which enables the economic modelling of ‘infinite domain’ type problmes. A typical problem is an opening in a stress field in an infinite medium, either in two or three dimensions. The strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of ‘infinite domain’ elements. Several sample problems has been analysed for circular, square and spherical openings in infinite media, and the results compared with either theoretical or boundary element solutions which include the ‘infinite’ boundary in their solution technique.     

Similitude of sandwich panels with a ‘soft’ core in buckling

The paper presents the similarity analysis of a sandwich unidirectional panel with a transversely flexible core under buckling loads. The governing equations are those used in the high-order analysis of sandwich panels with a ‘soft’ core. The study derives the similitude conditions in the case of external in-plane compressive loads that yield buckling of the panel with and without imperfections. In the first part, the buckling analysis is presented and it is based on the linearized version of the governing equations of the non-linear geometrical bending equations. The presentation includes an analytical proof of the applicability of similarity for the buckling of a sandwich panel with identical faces and a numerical demonstration of the response when full similarity and partial similarity exist. The effects of full and partial similarity are presented for a panel with imperfections.     

An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates

A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.     

Supertough wear-resistant coatings with ‘chameleon’ surface adaptation

The chameleon's ability to change skin color depending on environment to increase its chances of surviving served as an inspiration in the development of self-adaptive supertough wear-resistant coatings. Surface chemistry, structure and mechanical properties of these thin (0.5 μm) coatings reversibly change with applied load and environment, providing the best wear protection. Coating designs developed in-house are reviewed together with a critical analysis of design reports in the literature. ‘Chameleon’ coatings were prepared using novel nanocomposite structures, consisting of crystalline carbides, diamond-like carbon (DLC), and transition metal dichalcogenides. Various mechanisms were activated to achieve surface self-adaptation and supertough characteristics. They included: transition of mechanical response from hard and rigid to quasi plastic by grain boundary sliding at loads above the elastic limit; friction induced sp³→sp² phase transition of the DLC phase; re-crystallization and reorientation of the dichalcogenide phase; change of surface chemistry and structure from amorphous carbon in humid air to hexagonal dichalcogenide in dry nitrogen and vacuum; and sealing the dichalcogenide phase to prevent oxidation. These mechanisms were demonstrated using WC/DLC, TiC/DLC, and WC/DLC/WS₂ coatings. The hardness of WC/DLC and TiC/DLC composites was between 27–32 GPa and scratch toughness was 4–5 fold above that of nanocrystalline carbides. The WC/DLC/WS₂ composites survived millions of sliding cycles in vacuum and air under 500–1000 MPa loading, and exhibited excellent friction recovery in humid↔dry environmental cycling. Their friction coefficients were about 0.1 in humid air, 0.03 in vacuum, and as low as 0.007 in dry nitrogen. The proposed ‘chameleon’ concept can dramatically increase wear-resistant coating applicability, durability, and reliability.     

Complicating the ‘logic of design’

A ‘logic of design’ was outlined by March in 1976. Since then it has gained wide acceptance among designers and recently has been used in several knowledge-based systems of design. This paper makes a suggestion for extending the model by taking into consideration the logical nature of the laws in the argument form. This focus on the logical nature of laws brings out interesting and subtle differences in the inference process which are lost in the current analysis. It also results in some interesting complications. It means that it is no longer adequate to talk of the three phases of design — performance prediction, knowledge acquisition, and design generation — in the simple categories of deduction, induction and abduction, respectively. In particular, it means that performance prediction is not necessarily (or even usually) a deductive inference.     

Load combination analysis by ‘Directional simulation in the load space’

The reliability of structures subjected to multiple time-varying random loads is considered herein. It is well-known that the reliability of such systems may be evaluated by considering outcrossings of the load process vector out of a safe domain, and the contribution of individual loads to structural failure may be evaluated by considering outcrossings caused by combinations of one or more loads. In this paper the ‘Directional Simulation in the Load Space’ approach to reliability analysis is developed to consider explicitly outcrossings caused by all possible combinations of loads, during analysis of systems comprising stationary continuous Gaussian loads. To do this, the direction of the load process vector is ‘fixed’ at each point of outcrossing (to physically represent the particular combination of loads causing the outcrossing), and, by considering each possible load combination, all loads not causing an outcrossing are then held constant during radial integration (to model correctly that they do not contribute to each outcrossing). A numerical example demonstrating the validity of the proposed formulation is presented.     

Direct analysis of elastic–plastic structures with ‘overlay’ materials during cyclic loading

Several computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub-elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub-elements exhibiting all, however, the same total strain.¹,² In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic-plastic structures with kinematic hardening material,³ and we extended to some elastic viscoplastic ones,⁴ can easily be applied to these particular ‘overlay’ materials. One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.     

Economical experimentation via ‘lean design’

In industrial applications of design of experiments, practical constraints in resources such as budget, time, materials and manpower could lead to difficulties in completing an experiment even of moderate size. This problem can be addressed by an approach referred to as ‘lean design’, with which no more than a bare minimum number of response values are required, and the results of a lean design experiment can be improved incrementally up to a point identical to what can be obtained from a regular design. A numerical example illustrates both the principles and applications of this cost-effective approach to experimentation.