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25 articles for “trigonometric”
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Artificial Intelligence in Trigonometry: Innovations, Applications, and Future Prospects
Abstract: Artificial Intelligence (AI) has transformed numerous scientific fields, yet its integration with classical mathematics such as trigonometry is still emerging. This paper explores how AI enhances trigonometric problem solving, learning, and real-world applications. We analyse AI-driven tools for teaching trigonometry, AI in geometric and spatial reasoning, usage in robotics and computer vision, and future directions for research. Key challenges, methodologies, and case studies are discussed to provide a comprehensive overview …
Published in Journal of Artificial Intelligence Research & Advances · Vol. 13, Issue 3, 2025 Read article
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Thermal Analysis of Isotropic and Orthotropic Plate by Trigonometric Shear Deformation Theory
Abstract: In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates …
Published in Journal of Geotechnical Engineering · pp. 38–59 Read article
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Bending Analysis of Sandwich Beams According to Refined Trigonometric Beam Theory
Abstract: An equivalent single layer trigonometric shear deformation theory is presented for flexure of sandwich beams. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is assumed to be a function of longitudinal direction. Normal and shear strains corresponding to assumed displacement field of the present theory are obtained within the framework of linear theory of elasticity. …
Published in Journal of Aerospace Engineering & Technology · Vol. 5, Issue 3, 2015 · pp. 27–37 Read article
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Flexure and vibration of thick beams using trigonometric shear deformation theory
Abstract: A trigonometric shear deformation theory is used for flexural analysis of thick beams, taking into account transverse shear deformation effect. The theory accounts for cosine distribution of transverse shear strain through the thickness of the beam. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. The general solutions for the transverse displacement and rotation are presented for transversely loaded beams. The solutions for …
Published in Journal of Experimental & Applied Mechanics · Vol. 1, Issue 1, 2010 · pp. 1–27 Read article
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Flexure of Thick Cantilever Beams using Trigonometric Shear Deformation Theory
Abstract: A trigonometric shear deformation theory for flexural analysis of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses …
Published in Journal of Experimental & Applied Mechanics · Vol. 3, Issue 1, 2012 · pp. 17–31 Read article
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Free Vibration Analysis of Rectangular Plates using Two Variable Trigonometric Shear Deformation Theory
Abstract: In this paper, a two variable trigonometric shear deformation plate theory is developed for the free vibration analysis of thick isotropic square and rectangular plates. The theory involves only two unknowns, as against three in first order shear deformation theory and other higher order theories. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The transverse …
Published in Journal of Experimental & Applied Mechanics · Vol. 6, Issue 3, 2015 · pp. 58–64 Read article
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Thermo-mechanical Analysis of Orthotropic plate under Sinusoidally Distributed Thermal load by using Trigonometric shear Deformation Theory (TSDT)
Abstract: For the thermal analysis of simply supported square and rectangular plates applied to sinusoidal distributed linear thermal load throughout the plate thickness and in combination with sinusoidal distributed transverse mechanical loading, a trigonometric shear deformation theory is proposed. In this work, a sinusoidal function in terms of thickness coordinates is being used in the displacement field in conjunction with the transverse shear deformation effect. The normal and shear stress can …
Published in Journal of Experimental & Applied Mechanics Read article
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Thermo-mechanical Analysis of Orthotropic plate under Sinusoidally Distributed Thermal load by using Trigonometric shear Deformation Theory (TSDT)
Abstract: For the thermal analysis of simply supported square and rectangular plates applied to sinusoidaldistributed linear thermal load throughout the plate thickness and in combination with sinusoidaldistributed transverse mechanical loading, a trigonometric shear deformation theory is proposed. Inthis work, a sinusoidal function in terms of thickness coordinates is being used in the displacement fieldin conjunction with the transverse shear deformation effect. The normal and shear stress can bedetermined by using the …
Published in Journal of Experimental & Applied Mechanics · Vol. 12, Issue 3, 2021 · pp. 10–33 Read article
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Cylindrical Bending of Shear Flexible Plates Using Trigonometric Shear Deformation Theory
Abstract: A trigonometric shear deformation theory for cylindrical bending of shear flexible plates taking into account transverse shear deformation effect is developed. The displacement field of the theory uses sinusoidal function in terms of thickness coordinate to include shear deformation effects. It has only two variables. It is to be noted that the present theory satisfies the constitutive relations in respect of transverse shear strain and stress. The transverse shear stress …
Published in Journal of Experimental & Applied Mechanics · Vol. 3, Issue 2-3, 2012 · pp. 1–11 Read article
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Bidirectional Bending of Laminated Plates Using Trigonometric Shear Deformation Theory
Abstract: Bidirectional bending analysis of symmetric cross-ply laminated plates using trigonometric shear deformation theory is presented. Theory takes into account of transverse shear deformation effect without transverse strain effect. Theory uses sinusoidal function in the displacement field in terms of thickness coordinate to include shear deformation effects. It has only three variables. It is to be noted that the present theory satisfies the constitutive relations in respect of transverse shear strain …
Published in Journal of Experimental & Applied Mechanics · Vol. 4, Issue 1, 2013 · pp. 1–7 Read article
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A Discrete Layer Shear Deformation Theory for Flexure of Thick Cross-ply Laminated Beams
Abstract: A discrete layer shear deformation theory taking into account transverse shear deformation effects, is presented for flexure of two layered (90/0) cross ply laminated beams. The displacement field of the theory contains two variables. Theory does not require shear correction factor. The sinusoidal function is used in the displacement field in terms of thickness coordinate to represent shear deformation. Transverse shear stress can be obtained from the use of constitutive …
Published in Journal of Experimental & Applied Mechanics · Vol. 2, Issue 1, 2011 · pp. 1–16 Read article
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Thermal Stress Analysis of Cross-ply Laminated Plates using Refined Shear Deformation Theory
Abstract: A refined shear deformation theory is presented for laminated plates under thermal loading. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Stresses and deflections of isotropic, orthotropic, symmetric and antisymmetric cross- ply laminated plates subjected to linear thermal loads are obtained. It is to …
Published in Journal of Experimental & Applied Mechanics · Vol. 2, Issue 1, 2011 · pp. 47–66 Read article
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Thermal Analysis of Isotropic and Orthotropic Plate By Trignometric Shear Deformation Theory
Abstract: In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates …
Published in Journal of Geotechnical Engineering · Vol. 8, Issue 2, 2021 · pp. 38–59 Read article
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A Study on the Derivations of Two-dimensional Geometry
Abstract: Two-dimensional geometry is the study of conic sections. The conic section includes figures like circle, hyperbola, ellipse, parabola, semi circles etc. The study of two-dimensional geometry has many formulas related to Area, perimeter. However, the derivation of the particular geometrical figures are not studied due to their complexity. This paper focuses on how to reduce the complex nature of derivations and provides them in new and easy form. In addition, …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 1, 2020 · pp. 1–5 Read article
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Displacements in Thick Beams Using Refined Shear Deformation Theory
Abstract: Normal 0 false false false EN-US X-NONE X-NONE A trigonometric shear deformation theory for displacement of thick beams, by considering the transverse shear deformation effects, is presented. Variables in the present theory are same as that of in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. Governing differential equations and various boundary conditions …
Published in Journal of Aerospace Engineering & Technology · Vol. 4, Issue 3, 2014 · pp. 22–30 Read article
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Wrapped Fernandez and Steel's Skewed Laplace Distribution and its Applications in Ornithology
Abstract: In this paper, we introduce a new circular distribution called Wrapped Fernandez and Steel's Skewed Laplace distribution. We obtain explicit form for the density and derive expressions for distribution function, characteristic function and trigonometric moments. Method of maximum likelihood estimation is used for estimation of parameters. The proposed model is also applied to two real life data sets in ornithology and its performance is compared with that of wrapped Laplace …
Published in Research & Reviews : Journal of Statistics · Vol. 6, Issue 3, 2017 · pp. 73–83 Read article
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Strategic Solutions: How Mathematics Reshapes Industrial Landscapes
Abstract: One of the earliest and most fundamental fields of the physical sciences is mathematics. It has a significant impact on industrial enterprises' bottom lines and enhances their performance in the current data-driven market. One subfield of applied mathematics is industrial mathematics. It concentrates on issues that arise in the industry and seeks answers that are pertinent to the sector. The use of mathematical models and techniques to diverse industry difficulties …
Published in International Journal of Industrial and Product Design Engineering · Vol. 2, Issue 1, 2024 · pp. 16–23 Read article
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Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method
Abstract: Equations for non-linear evolution are mathematical representations of physical phenomena. The physical interpretation of the solution functions of these equations enhances the viewpoint of many natural processes. Numerous scientists who acknowledge this truth have focused on this area. These mathematical models are even more important since they provide light on a multitude of events when their solutions take on a physical significance. Through their research, numerous scientists create methods and …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 25–33 Read article
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The Contribution of Mathematics to Make Developed India
Abstract: This research paper explores the significant contributions of mathematics to the development of India, tracing its influence from ancient innovations to modern applications across diverse sectors. India has a long-standing mathematical tradition, with foundational achievements such as the invention of zero, the decimal system, and advancements in algebra, trigonometry, and geometry, which profoundly shaped global knowledge systems. These early contributions established India as a pioneering hub of mathematical thought and …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 08–15 Read article
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Xypher Bot: Autonomous Surveying Robot
Abstract: Xypher Bot is a fully autonomous robot built to carry out tasks like height measurement, estimating distance, and detecting objects. It uses affordable and easily available components such as the MPU6050 sensor, ultrasonic sensors, and a laser pointer. By using simple trigonometry, the bot can measure object height with good accuracy. The top part of the bot, which is responsible for height measurement, has already been built and tested. The …
Published in International Journal of Advanced Robotics and Automation Technology · Vol. 3, Issue 2, 2025 · pp. 49–62 Read article