Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

A model, based on the theory of nonlocal continuum mechanics, on the column buckling of multiwalled carbon nanotubes is presented. The present analysis considers that each of the nested concentric tubes is an individual column and that the deflection of all the columns is coupled together through the van der Waals interactions between adjacent tubes. Based on this description, a condition is derived in terms of the parameters that describe the van der Waals forces and the small internal length scale effects. In particular, an explicit expression is derived for the critical axial strain of a double walled carbon nanotube which clearly demonstrates that small scale effects contribute significantly to the mechanical behavior of multiwalled carbon nanotubes and cannot be ignored.

Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics

Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams

Bending of Euler–Bernoulli beams using Eringen’s integral formulation: A paradox resolved

Free vibration analysis of functionally graded size-dependent nanobeams

Closed form solution for a nonlocal elastic bar in tension

Nonlocal integral elasticity: 2D finite element based solutions

Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the internal length are conjectured to be each the cause of additional attenuation effects upon the long distance particle interactions. The increased attenuation effects are accounted for by means of the standard attenuation function, but with the standard spatial distance replaced by a suitably larger equivalent distance, and with the spatially variable internal length replaced by the largest value within the domain. Formulae for the computation of the equivalent distance are heuristically suggested and illustrated with numerical examples. The solution uniqueness of the continuum boundary-value problem is proven and the related total potential energy principle given and employed for possible nonlocal-FEM discretizations. A bar in tension is considered for a few numerical applications, showing perfect numerical stability, provided the free energy potential is positive definite.

A nonhomogeneous nonlocal elasticity model

A strain-difference-based nonlocal elasticity model

Mechanical fasteners, commonly used in many advanced engineering applications dealing with composite laminates, play the main role of transferring loads between the linked structural elements. The present study, focused on pinned-joints, explores the possibility of applying a direct method for evaluating the joint’s strength as well as for predicting some of the more common joint’s failure mechanisms. A limit analysis numerical approach for statically loaded pinned-joint orthotropic laminates in plane stress conditions is proposed. Two well known numerical procedures for limit analysis likewise having common roots, namely the Linear Matching Method and the Elastic Compensation Method, are utilized to evaluate upper and lower bounds to the joint collapse load. Both methods are rephrased assuming for the material in use a Tsai–Wu type yield surface. The results obtained are compared and plotted against some available experimental findings. Some final remarks draw attention to the potentialities and the limits of the proposed approach.

Aurora Angela Pisano

Papers

Closed form solution for a nonlocal elastic bar in tension

Nonlocal integral elasticity: 2D finite element based solutions

A nonhomogeneous nonlocal elasticity model

A strain-difference-based nonlocal elasticity model

Mechanically fastened joints in composite laminates: Evaluation of load bearing capacity