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The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.

The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.

Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

Global warming is a process that takes place 11,500 years after the end of the last Ice Age. The main identified reason is the increased emissions of greenhouse gases (GHGs). Since the nineteenth century, GHG evolution has recorded a quantum leap from the previous linear development. Human is the main factor behind this evolution, through industrialization and the exponential increase of population. Based on these, the chapter’s primary goal was to highlight an original method of predicting the future evolution of GHG emissions in the domains of Energy (including Transportation), Industry Processes and Product Use, Agriculture, and Waste Management. The novelty of the research consisted of testing several variants of functions (power, exponential, inverse trigonometric) to identify, from a group of variants. This optimal function would generate those predictions, which are closest to the real values. The causes that create GHG emissions in each of the four domains were the foundation for the analysis. This chapter focuses on two main subjects: first, the identification of a smooth function to predict the evolution of GHG emissions, and second, the function’s use to estimate the projections of GHG emissions in the coming years for the four domains: Energy (including Transportation), Industry Processes and Product Use, Agriculture, and Waste Management. An observation was that the weights of these four domains remain relatively the same despite the reductions in the total GHG emissions.

The purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO₂) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work.

In this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle.

The bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences.

For the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

The purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.

Thermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.

Critical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.

The temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

The purpose of this paper is to present the design and analysis of a robotic finger mechanism for robust industrial applications.

The resultant design is a compact rigid link finger, which is adaptive to different shapes and sizes providing necessary grasping features. A number of such fingers can be assembled to function as a special purpose end effector.

The mechanism removes a number of significant problems usually experienced with tendon‐based designs. The finger actuation mechanism forms a compact and positive drive unit within the end effector's body using solid mechanical linkages and integrated actuators.

The paper discusses the design issues associated with a limited number of actuators to operate in a constrained environment and presents various considerations necessary to ensure safe and reliable operations.

The design is original in existence and developed for special purpose handling applications that offers a strong and reliable system where space and safety is of prime concern.

Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. The purpose of this paper is to automate this translation. This paper uses Maple and Mathematica as the CAS, and LaTeX as the DPS.

Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special LaTeX macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). The authors are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, the authors develop software to ease the creation of new rules and to discover inconsistencies.

The authors created 396 mappings and translated 58.8 percent of DLMF formulae (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. An atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. The evaluation techniques discovered two errors in the DLMF and one defect in Maple.

This paper introduces the first translation tool for special functions between LaTeX and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.

There have been large changes in the content of chemistry courses during the post‐war period, particularly at an advanced level. It is believed that the relevance of the existing mathematics course to the changing chemistry syllabus and to what industry expects of the trained chemist is sometimes neglected. This has led (in Constantine College) to a reconsideration of the adequacy of syllabuses in mathematics for existing advanced chemistry courses and to a consideration of the type of course which would be attractive to the industrial chemist. The authors have been supported by a working party and the ideas suggested here result largely from its findings. The object of this paper is to put forward some views as a first approximation in the hope that this will stimulate discussion and criticism of the existing situation. In November of 1964 a two‐day course was held in Newcastle on the teaching of physical chemistry. The lecturers at this meeting were mainly from university departments plus one industrialist and one former university lecturer now at a government research institute. Letters were sent to seven of these lecturers, who were asked what mathematics they considered appropriate for a modern undergraduate chemistry course. Most of the replies indicated what mathematics was being taught to chemistry undergraduates in the department with which the writer was concerned. In addition some information was volunteered by one other university department. In the non‐industrial replies topics were mentioned with a frequency indicated by the number following each topic — calculus (6), matrices and determinants (6), group theory and symmetry (4), vectors (4), differential equations (4) and probability (3). The industrial reply was quite different and discussed the need for the chemist to have an understanding of more industrial mathematics.

In the mining industry, a run-of-mine (ROM) stockpile is a temporary storage unit, but it is also widely accepted as an effective method to reduce the short-term variations of ore grade. However, tracing ore grade at ROM stockpiles accurately using most current fleet management systems is challenging, due to insufficient information available in real time. This study aims to build a three-dimensional (3D) model for ROM stockpiles continuously based on fine-grained grade information through integrating data from a number of ore grade tracking sources.

Following a literature review, a framework for a new stockpile management system is proposed. In this system, near real-time high-resolution 3D ROM stockpile models are created based on dump/load locations measured from global positioning system sensors. Each stockpile model contains a group of layers which are separated by different qualities.

Acquiring the geometric shapes of all the layers in a stockpile and cuts made by front wheel loaders provides a better understanding about the quality and quality distribution within a stockpile when it is stacked/reclaimed. Such a ROM stockpile model can provide information on predicating ore blend quality with high accuracy and high efficiency. Furthermore, a 3D stockyard model created based on such ROM stockpile models can help organisations optimise material flow and reduce the cost.

The modelling algorithm is evaluated using a laboratory scaled stockpile at this stage. The authors expect to scan a real stockpile and create a reference model from it. Meanwhile, the geometric model cannot represent slump or collapse during reclaiming faithfully. Therefore, the model is expected to be reconcile monthly using laser scanning data.

The proposed model is currently translated to the operations at OZ Minerals. The use of such model will reduce the handling costs and improve the efficiency of existing grade management systems in the mining industry.

This study provides a solution to build a near real-time high-resolution multi-layered 3D stockpile model through using currently available information and resources. Such novel and low-cost stockpile model will improve the production rates with good output product quality control.

Nonlinear model predictive control (NMPC) is emerging as a way to control unmanned aircraft with flight control constraints and nonlinear and unsteady aerodynamics. However, these predictive controllers do not perform robustly in the presence of physics-based model mismatches and uncertainties. Unmodeled dynamics and external disturbances are unpredictable and unsteady, which can dramatically degrade predictive controllers’ performance. To address this limitation, the purpose of this paper is to propose a new systematic approach using frequency-dependent weighting matrices.

In this framework, frequency-dependent weighting matrices jointly minimize closed-loop sensitivity functions. This work presents the first practical implementation where the frequency content information of uncertainty and disturbances is used to provide a significant degree of robustness for a time-domain nonlinear predictive controller. The merit of the proposed method is successfully verified through the design, coding, and numerical implementation of a robust nonlinear model predictive controller.

The proposed controller commanded and controlled a large unmanned aerial system (UAS) with unsteady and nonlinear dynamics in the presence of environmental disturbances, measurement bias or noise, and model uncertainties; the proposed controller robustly performed disturbance rejection and accurate trajectory tracking. Stability, performance, and robustness are attained in the NMPC framework for a complex system.

The theoretical results are supported by the numerical simulations that illustrate the success of the presented technique. It is expected to offer a feasible robust nonlinear control design technique for any type of systems, as long as computational power is available, allowing a much larger operational range while keeping a helpful level of robustness. Robust control design can be more easily expanded from the usual linear framework, allowing meaningful new experimentation with better control systems.

Such algorithms allows unstable and unsteady UASs to perform reliably in the presence of disturbances and modeling mismatches.