Euripidis Mistakidis

Fractal geometry and fractal material behaviour in solids and structures

SummaryThe present paper discusses certain methods which permit us to consider the influence of the fractal geometry and the fractal material behaviour in solid and structural mechanics. The method of fractal interpolation function is introduced and the fractal quantities (boundary geometry, interface geometry and stress-strain laws) are considered as the fixed points of a given set-valued transformation. Our first aim here is to define the mechanical quantities on fractal sets using some elementary results of the theory of Besov spaces. Then we try to extend the classical finite element method for the case of fractal bodies and fractal boundaries and corresponding error estimates are derived. The fractal analysis permits the formulation and the treatment of complicated or yet unsolved problems in the theory of deformable bodies.ÜbersichtDiskutiert werden Methoden, die es erlauben, den Einfluß von fraktaler Geometrie und fraktalem Materialverhalten in der Festkörper- und Strukturmechanik zu betrachten. Die Methode der fraktalen Interpolationsfunktion wird eingeführt; die fraktalen Größen (Randgeometrie, Grenzflächengeometrie und Spannungs-Dehnungsgesetze) werden als Fixpunkte einer gegebenen mengenwertigen Transformation betrachtet. Das erste Ziel ist die Definition der mechanischen Größen auf fraktalen Mengen, wofür einige grundlegende Ergebnisse der Theorie der Besov-Räume herangezogen werden. Weiterhin wird die klassische Finite-Element-Methode auf fraktale Körper und fraktale Ränder erweitert und zugehörige Fehlerabschätzungen werden abgeleitet. Die fraktale Betrachtung gestattet die Formulierung und Behandlung komplizierter oder noch ungelöster Probleme der Theorie deformierbarer Körper.

Dependence of contact area on the resolution of fractal interfaces in elastic and inelastic problems

Purpose – The purpose of this paper is to investigate the influence of the resolution with which interfaces of fractal geometry are represented, on the contact area and consequently on the contact interfacial stresses. The study is based on a numerical approach. The paper focuses on the differences between the cases of elastic and inelastic materials having as primary parameter the resolution of the interface.Design/methodology/approach – A multi‐resolution parametric analysis is performed for fractal interfaces dividing a plane structure into two parts. On these interfaces, unilateral contact conditions are assumed to hold. The computer‐generated surfaces adopted here are self‐affine curves, characterized by a precise value of the resolution δ of the fractal set. Different contact simulations are studied by applying a horizontal displacement s on the upper part of the structure. For every value of s, a solution is taken in terms of normal forces and displacements at the interface. The procedure is repeat...

Numerical study of low‐yield point steel shear walls used for seismic applications

Purpose – The purpose of this paper is to provide the research and practising engineers with insight on the benefits of using low‐yield point steel with respect to ordinary steel as a construction material for shear wall panels. The paper seeks to focus on the behaviour of such panels when installed in new or existing structures in order to improve their seismic performance.Design/methodology/approach – Finite element models are applied in order to approximate the structural response of low‐yield steel panels, used for seismic applications. Owing to the specific characteristics of the problem at hand, geometric and material nonlinearities have to be accurately considered. For comparison reasons, low‐yield point steel and ordinary steel are considered as construction materials for the aforementioned panels. The paper examines both the case of “pure shear” steel panel and also the more realistic case that the panel is encased in the surrounding frame.Findings – The paper reaches a number of interesting conc...

On the numerical solution of structures with fractal geometry: The FE approach

The scope of the present paper is to present the numerical aspects of the theory developed in [1]. The fractal geometry of structure(s) is approximated either through the IFS (iterated function system) method or through the FI (fractal interpolation) method. These approximations of the fractal through classical curves and surfaces are combined with the FEM in order to get numerical results for important technical problems, which cannot be satisfactorily treated by other methods.SommarioLo scopo del lavoro é quello di discutere gli aspetti numerici della teoria sviluppata in [1]. La geometria frattale della/e struttura é approssimata sia attraverso il metodo IFS (iterated function system) che il metodo FI (fractal interpolation). Queste approssimazioni frattali, attraverso curve e superfici classiche, sono combinate con il metodo degli elementi finiti, onde potere ottenere risultati numerici per importanti problemi tecnici che non potrebbero venire soddisfacentemente affrontati con altri metodi.

Nonconvex Optimization in Mechanics: Algorithms, Heuristics and Engineering Applications

Part I: Nonconvexity in Engineering Applications. 1. Nonconvexity in Engineering Applications. Part II: Applied Nonconvex Optimization Background. 2. Applied Nonconvex Optimization Background. Part III: Superpotential Modelling and Optimization in Mechanics with and without Convexity and Smoothness. 3. Convex Superpotential Problems. 4. Nonconvex Superpotential Problems. 5. Optimal Design Problems. Part IV: Computational Mechanics. Computer Implementation, Applications and Examples. 6. Computational Mechanics Algorithms. 7. Applications. Index.

Computational modeling of high performance cementitious thin shell elements under in-plane shear

ABSTRACT High-performance cementitious materials are widely used in the construction of thin shell elements. This study investigates a simulation method based on composite layered shells for the nonlinear analysis of high-performance cementitious elements under in-plane shear. A tube torsion test is simulated and analyzed with MSC-MARC and its results are compared to an alternative calculation method, the Simplified Model for Combined Stress resultants (SMCS), as well as with experimental data. The simulation method is found to produce accurate results for fully under-reinforced elements with a range of strong to weak reinforcement ratios less than 2.

Hemivariational Inequality Modeling of Hybrid Laminates with Unidirectional Composite Constituents

Theoveralltensileandbendingbehaviorofunidirectionalcompositeelementswithmonotoneandnonmonotone, possibly multivalued,constitutive laws foreach constituent arestudied within a nonsmooth mechanics framework. A nondifferentiable and possibly nonconvex, caused by degradation effects, potential energy is formulated for the whole mechanical system. For the structural analysis problem the potential energy minimization problem is considered. The arising variational or hemivariational (in the case of nonmonotone laws ) inequality problems are solved by appropriate nonconvex-nonsmooth computational mechanics techniques. Parametric numerical investigations of typical composite elements are presented, which shed light into the complex behavior of the composite structural elements. On the other hand, the arising overall laws can be used as phenomenological laws for structural analysis of large-scale structures incorporating the studied composite elements. I. Introduction C OMPOSITE materials is a rapidly maturing technology with emerging applications in a wide range of industries far beyond the aerospace domain where they e rst became popular. Nowadays, composites are popular even in the civil-engineering domain and are used for the construction of light bridges, domes, space trusses, etc. Moreover, composite elements are used in structures that are susceptible to electrochemical actions or corrosion, such as underground facilities, offshore oil platforms, waterways, and harbors. 1 The basic principles involved in the design of structures made of compositematerialsarethesameasthoseofisotropicmaterialssuch as steel. The classical theories and methods of analysis can be used for the design ofcomposite structures, asfar as the constitutive relationship takes into account the material anisotropy and the strength degradation effects, which are present in the majority of composite materials. Moreover, the same basic design knowledge and technique used for other materials as, e.g., for reinforced concrete, can be applied to compositestructures.However, thereader shouldhave inmindthattheimplementationofaccuratedesignmethodsforsteel (which is the materialwith the most simple constitutive relationship used today in civil-engineering structures ) has required a century of research and experience. In this framework it is not only very important to study these new materials at the materials level, but it is also very important to know their behavior at the structural level. (Compare in this respect the combined effects in the study of beam-to-column connections in steel structures, which lead to strong nonlinearities.) Also, the phenomenological (macroscopic ) response under certain types of loading is of great importance. In unidirectional composites the e bers are aligned in one only direction, thus achieving the maximum e ber alignment and the maximum e ber content. As in principle, the strength of a composite structural element increases in proportion to increasing e ber content, this type of composite provides high strength to the direction of the e bers but very low transverse strength. Therefore it is very common to combine unidirectional composite materials in a cer

Interface modelling between CFD and FEM analysis: the dual-layer post-processing model

Purpose The primary purpose of this paper is the development of a fire–structure interface (FSI) model, which is referred in this study as a simplified “dual-layer” model. It is oriented for design purposes, in the cases where fire-compartments exceed the “regular” dimensions, as they are defined by the guidelines of the codes (EN 1991-1-2). Design/methodology/approach The model can be used at the post-processing stage of computational fluid dynamics (CFD) analysis and it is based on the gas-temperature field (spatial and temporal) of the fire-compartment. To use the “dual-layer” model, first the gas-temperature (discrete) function along the height of the fire-compartment, at discrete plan–view points should be determined through the output of the CFD analysis. The model “compresses” the point data to (spatial) virtual zones, which are divided into two layers (with respect to the height of the fire-compartment) of uniform temperature: the upper (hot) layer and the lower (cold) layer. Findings The model calculates the temporal evolution of the gas-temperature in the fire compartment in every virtual zone which is divided in two layers (hot and cold layer). Originality/value The main advantage of this methodology is that actually only three different variables (height of interface upper-layer temperature and lower-layer temperature) are exported during the post-processing stage of the CFD analysis, for every virtual zone. Next, the gas-temperature can be used for the determination of the temperature profile of structural members using simple models that are proposed in EN 1993-1-2.

A study on the dependency of the interface forces on the FE discretization in nonconvex‐nonsmooth frictional contact problems

In this paper, the effect of the FE discretization density on the results of both convex and nonconvex‐nonsmooth frictional contact and adhesive contact interface problems is investigated. The tool for this study is a variational formulation leading to an iterative method for the numerical solution of the arising nonconvex‐nonsmooth optimization problems. Various cases of monotone and nonmonotone interface laws are considered and interesting results are obtained.

Parametric Analysis of Axially Loaded RHS Gap K-Joints by Means of 2-D and 3-D F.E. Models

In the present paper the behaviour of steel structural RHS gap K-joints under static loading is studied by applying the Finite Element Method. The analysis is performed by the development of both 2-D and 3-D models of gap K-joints, thus investigating the influence of certain geometrical parameters into the strength and the overall stability of the joint. The geometry of the analyzed joints is in agreement with the general requirements of the EC3. The obtained results are compared to those obtained using the EC3–Annex K calculation formulas and the respective conclusive remarks are presented in the last part of the paper.