Use Of Higher-order Theory Research Articles

Two novel Kirchhoff plate finite elements for the modified strain gradient theory

AbstractMicroplates are vastly used in MEMS and NEMS devices. Due to size effect, classical theories of continuum mechanics can not be used to model mechanical behaviour of them. Instead, higher order continuum theories should be implemented. Modified Strain Gradient Theory (MSGT) is considered to be one of the most accurate methods for this, considering both theoretical compatibility and numerical accuracy. In this study, two sets of Kirchhoff and twist‐Kirchhoff bending rectangular plate finite elements for MSGT are developed as novel aspects. This is done by first obtaining the weak forms by using variational methods and then deriving the set of algebraic equations for the finite element formulation starting with shape functions. Although non‐conforming, the finite elements are in alignment with the existing models with the given length scale parameters. The plate finite elements are then implemented to existing models. The length scale parameters for MSGT are also identified for gold using the existing experimental results in literature. This study proposes the use of higher order theories for gold microplates for thicknesses less than 40 µm.

Training the use of theory of mind using artificial agents

When engaging in social interaction, people rely on their ability to reason about unobservable mental content of others, which includes goals, intentions, and beliefs. This so-called theory of mind ability allows them to more easily understand, predict, and influence the behavior of others. People even use their theory of mind to reason about the theory of mind of others, which allows them to understand sentences like ‘Alice believes that Bob does not know about the surprise party’. But while the use of higher orders of theory of mind is apparent in many social interactions, empirical evidence so far suggests that people do not use this ability spontaneously when playing strategic games, even when doing so would be highly beneficial. In this paper, we attempt to encourage participants to engage in higher-order theory of mind reasoning by letting them play a game against computational agents. Since previous research suggests that competitive games may encourage the use of theory of mind, we investigate a particular competitive game, the Mod game, which can be seen as a much larger variant of the well-known rock–paper–scissors game. By using a combination of computational agents and Bayesian model selection, we simultaneously determine to what extent people make use of higher-order theory of mind reasoning, as well as to what extent computational agents can encourage the use of higher-order theory of mind in their human opponents. Our results show that participants who play the Mod game against computational theory of mind agents adjust their level of theory of mind reasoning to that of their computer opponent. Earlier experiments with other strategic games show that participants only engage in low orders of theory of mind reasoning. Surprisingly, we find that participants who knowingly play against second- and third-order theory of mind agents apply up to fourth-order theory of mind themselves, and achieve higher scores as a result.

A comparative study of modified strain gradient theory and modified couple stress theory for gold microbeams

Microbeams are common structures encountered in micro- and nano-electromechanical systems. Their mechanical response cannot be modelled by local theories of continuum mechanics due to size effect, which becomes more pronounced as the structural length scale approaches the microstructural length scale. The size effect can be circumvented by higher-order continuum theories. In this study, Euler–Bernoulli microbeams are analysed with modified strain gradient theory (MSGT) and modified couple stress theory (MCST). The weak forms for the numerical implementation are obtained by using variational methods. Then, the set of algebraic equations for the finite element method are derived. As a novel aspect, the performance of MSGT and MCST is compared and the length scale parameters of these theories are identified for gold microbeams from the existing experimental results in the literature. With the help of the identified parameters, the cut-off point for the applicability of the classical beam theories for gold microbeams is assessed. The study suggests use of higher-order theories for the state-of-the-art gold microbeam structures having thickness $$t<30\,\upmu {\hbox {m}}$$ .

Estimating the Use of Higher-Order Theory of Mind Using Computational Agents

Abstract When people make decisions in a social context, they often make use of theory of mind, by reasoning about unobservable mental content of others. For example, the behavior of a pedestrian who wants to cross the street depends on whether or not he believes that the driver of an oncoming car has seen him or not. People can also reason about the theory of mind abilities of others, leading to recursive thinking of the sort ‘I think that you think that I think…’. Previous research suggests that this ability may be especially effective in simple competitive settings. In this paper, we use a combination of computational agents and Bayesian model selection to determine to what extent people make use of higher-order theory of mind reasoning in a particular competitive game known as matching pennies. We find that while many children and adults appear to make use of theory of mind, participants are also often classified as using a simpler reactive strategy based only on the actions of the directly preceding round. This may indicate that human reasoners do not primarily use their theory of mind abilities to compete with others.

Analysis of Gold Microbeams with Higher Order Continuum Theories

AbstractMicrobeams are building blocks for many microstructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects based on their micro‐scale. These size effects can be taken into account by the so‐called higher order continuum theories. Modified Strain Gradient Theory (MSGT) and Modified Couple Stress Theory (MCST) are two commonly used theories, which extend the classical local continuum theories of grade one with the introduction of additional length scale parameters. In this contribution, the variational problem governing the elasticity of higher order beam formulation and the finite element implementation based upon, are briefly introduced. To this end, well known Euler‐Bernoulli beam formulation assumptions are used. The size effect for gold‐micro beams is demonstrated and the length scale parameters of gold microbeams for MSGT and MCST are identified form the existing experimental data from literature for the first time. As a novel aspect, significant size effect is demonstrated for the length‐scales associated with the state of the art gold microbeam structures developed for MEMS applications, which reveals the necessity of the use of higher order theories at these length scales. Advantages and drawbacks of these theories are also identified. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

ANALYSIS OF GOLD MICRO-BEAMS WITH MODIFIED STRAIN GRADIENT THEORY

Micro-beams are building blocks for many micro- and nano-structures as well as micro-electro-mechanical systems (MEMS) and cannot accurately be modeled by classical continuum theories due to significant size effects at the length scales associated with these structures. Size effects can be taken into account by the so-called higher order continuum theories. In this study, Euler-Bernoulli micro-beams are analyzed with the Modified Strain Gradient Theory (MSGT), which extends the classical local continuum theories of grade one with the introduction of three additional length scale parameters. In this contribution, finite element implementation is briefly demonstrated by using Galerkin discretization techniques for Euler-Bernoulli beams. The size effect for gold-micro beams is demonstrated and the length scale parameters of gold micro-beams for MSGT are identified form the existing experimental data from literature for the first time . As a novel aspect, significant size effect is demonstrated for the length-scales associated with the state of the art gold micro-beam structures developed for NEMS and MEMS applications, which reveals the necessity of the use of higher order theories at these length scales.

Higher-order shear deformation of very thick simply supported equilateral triangular plates under uniform load

ABSTRACTWhere deflections of thick plates are concerned, sufficient studies have been performed on circular and rectangular plates using first-order shear deformation theory (FSDT). Less attention, however, has been placed on the use of higher-order theories and plates of other shapes. This article proposes a deflection model for a simply supported and under uniformly loaded equilateral triangular plate that fulfils the third-order shear deformation theory (TSDT). Comparison of maximum plate deflections using this exact TSDT model with the FSDT and the simplified TSDT models reveals that the former exhibits better correlation agreement with the exact TSDT. Using the plate deflection from the exact TSDT, a refined shear correction factor, which is a function of Poisson's ratio, relative thickness, and location on plate, is extracted for the FSDT model. Results suggest that the usual shear correction model of 5/6 in Mindlin plates is highly accurate when dealing with moderately thick triangular plates made from negative Poisson's ratio materials, while the prescription of the refined shear correction factor obtained herein is advised for very thick triangular plates made from large Poisson's ratio materials. The results avail an FSDT deflection model for very thick triangular plates with the accuracy of exact TSDT.

On approximate solutions for the deformation of plane anisotropic beams

Plane deformation of anisotropic beams with narrow rectangular cross sections exhibits coupling of stretching, bending and transverse shearing. For anisotropic cantilever beams with a stiff end-cap under end forces and an end couple, assessments were made for approximate solutions by comparing these with numerically exact finite element (FE) solutions. Specific attention is given to point-wise or approximate satisfaction of the end-fixity conditions. As approximate methodologies, (i) the elementary polynomial form of Airy's stress function for the plane stress problem in a rectangular region, (ii) a Timoshenko-type beam theory, and (iii) the Bernoulli-Euler beam theory were selected. Among these, only the polynomial form of Airy's stress function violates the point-wise end-fixity conditions. Both the polynomial Airy stress function and the Timoshenko-type beam theory successfully model the effects of transverse shear deformation and the coupling of stretching and transverse deflection. Analytical solutions demonstrate that the normal shear coupling effect increases linearly with the thickness-to-span ratios in axial normal stress and axial displacement, while the coupling manifests quadratically in transverse displacement. The comparison of end displacements with the numerically exact FE solutions indicates that the polynomial form of Airy's stress function is no better than the Timoshenko-type beam theory. Similar conclusions were reached for the problem of uniformly loaded cantilever beams. It has been found that the accurate prediction of the deformation of thick anisotropic beams with significant normal-shear coupling requires the use of higher order theories.