There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Intermolecular And Surface Forces

Nonlinear Oscillations: Exact Solutions and their Approximations

https://pureadmin.qub.ac.uk/ws/files/126683921/Edited_sudagar_R1.pdf

Electroless nickel, alloy, composite and nano coatings – A critical review

In the present work, a normally loaded contact between a radially functionally graded hemisphere and a rigid flat is analysed in perfect slip condition for different values of gradient/inhomogeneity parameter. The analysis was performed with an axisymmetric model in commercial finite element software ANSYS 18.2. The Young's modulus, yield strength and tangent modulus (for bilinear isotropic hardening) are varied according to an exponential function. The effect of the inhomogeneity parameter on different contact behaviours, e.g., contact area, contact pressure, contact stresses, etc., of the hemisphere are obtained. Stress and deformation behaviour of the contact interface as well as of the entire hemisphere has been analysed. It is observed that for negative inhomogeneity parameter, while being deformed by the rigid flat, the summit of the hemisphere loses contact with flat and sinks in to have a concave shape at the top of the hemisphere. This phenomenon has not been reported in established literature yet.

Finite element-based contact analysis of a radially functionally graded hemisphere and a rigid flat

The chapter consists of static and dynamic analyses of a fractal rough surface in contact with a rigid flat. The fractal surface is constructed using modified Weierstrass-Mandelbrot function. A rigid flat surface touches the topmost point of the rough surface, which moves towards the rough surface and deforms it. Different contact parameters (e.g., contact force, contact area, contact stress, etc. for varying fractal and material properties are obtained through finite element based static analysis. A parameter denoting the degree of nonlinearity of the contact system is extracted from the force-displacement plot of the surface. This parameter is utilized to explain the dynamic behaviour of the fractal surface which vibrates under the influence of the externally excited rigid flat surface. The dynamic analysis of the contact system is carried out by modelling the contact interface as a single degree of freedom (SDOF) spring-mass-damper system. The dynamic behavior of the system is investigated in terms of frequency response curves, time-displacement plots, and phase plots.

Static and Dynamic Analysis of Deformable Fractal Surface in Contact With Rigid Flat

A corrosion and tribo-failure analysis of Ni-P-Cu coated mild steel (AISI-1040) at varied copper concentration

A numerical study of adhesive contact between rough surfaces with soft coating is presented using an elastic-plastic model of asperity contact deformation. The analysis considers the elastic and plastic deformation of both the coating and the substrate unlike the work available in literature where the coating is considered to be in pure plastic contact. The JKR (Johnson-Kendall-Roberts) adhesion model is used and the well-established adhesion indices (elastic and plastic adhesion indices) are utilized to consider the different conditions of varying load and material and surface properties of the substrate and the coating. Contact load and contact area are obtained as functions of mean separation between surfaces for different combinations of adhesion parameters, material properties and thickness of the coating. The effects of these parameters on contact behavior of coated surfaces are investigated. For thin coating and light loading, contact is strongly influenced by the existence of soft coating that increases the contact area due to plastic deformation of the coating.

Elastic-Plastic Adhesive Contact of Rough Surfaces with Soft Coatings

Experimental investigation and simulation study of different types of concentrically stiffened plates under static and dynamic conditions are accomplished in the present paper with an objective to establish the static deflection and natural frequency characteristics under loading. One unstiffened plate and five types of concentrically stiffened plate specimens are experimented upon in the laboratory with the help a specialized setup that simulates clamped end condition at the plate edges. There is provision for pneumatic application of transverse uniformly distributed load. The above-mentioned plate specimens are categorized on the basis of number and arrangement of the concentric stiffeners on the plate face. Finite element simulation is also performed through commercial software ANSYS Mechanical APDL 15.0 for independent validation and comparison of experimental data. Load–deflection plots and backbone curves in non-dimensional planes are presented as results.

Prasanta Sahoo

Papers

Finite element-based contact analysis of a radially functionally graded hemisphere and a rigid flat

Static and Dynamic Analysis of Deformable Fractal Surface in Contact With Rigid Flat

A corrosion and tribo-failure analysis of Ni-P-Cu coated mild steel (AISI-1040) at varied copper concentration

Elastic-Plastic Adhesive Contact of Rough Surfaces with Soft Coatings

Experimental Investigation on Static and Free Vibration Behavior of Concentrically Stiffened Plates