Large deformation analysis of functionally graded shells

AbstractA geometrically nonlinear analysis of functionally graded shells is presented. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. A tensor-based finite element formulation with curvilinear coordinates and first-order shear deformation theory are used to develop the functionally graded shell finite element. The first-order shell theory consists of seven parameters and exact nonlinear deformations and under the framework of the Lagrangian description. High-order Lagrangian interpolation functions are used to approximate the field variables to avoid membrane, shear, and thickness locking. Numerical results obtained using the present shell element for typical benchmark problem geometries with functionally graded material compositions are presented

Fonksiyonel Kademelendirilmiş Dairesel Plakların Lineer Olmayan Termomekanik Analizleri

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Bu çalışmada, mekanik ve ısıl yüklemelere maruz fonksiyonel kademelendirilmiş dairesel plakaların geometrik lineer olmayan analizleri yapıldı. Analizlerde Green-Lagrange şekil değiştirme tensörü kullanıldı. Kademelendirilmiş bölgedeki lokal malzeme özelliklerinin hesaplanmasında mikromekanik model olarak Mori-Tanaka şeması kullanıldı. Isıl yüklemeye maruz plakalarda kalınlık boyunca sıcaklık dağılımı sürekli rejim ısı transferi denklemi çözülerek tespit edildi. Örnek olarak da Zirkonya (ZrO2) ve Alüminyumdan (Al) oluşan fonksiyonel kademelendirilmiş dairesel plaka kullanıldı ve elde edilen sonuçlar grafik olarak sunuldu.In this study, geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads was carried out. The Green-Lagrange strain tensor in its entirety was used in the analysis. The locally effective material properties were evaluated using homogenization method that is based on the Mori-Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness was determined by solving a steady-state heat transfer (i.e., energy) equation. As an example, an FGM circular plate composed of Zirconium (ZrO2) and Aluminum (Al) was used and results are presented in graphical form

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeometric analysis

The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C2-continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton’s iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates

Vibration of Timoshenko Beams Using Non-classical Elasticity Theories

This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases

Pullout characteristics of functionally graded and degraded adhesive anchors

Three-dimensional axisymmetric elasticity solutions for pull-out stresses in bonded anchors with spatially stiffness-varying adhesive are presented. A stiff rod embedded in a semi-infinite rigid half-space through an adhesive layer, representing a general anchor problem is analysed. The adhesive layer is considered to have a smoothly varying stiffness over the entire or a portion of the embedded length. Two cases of particular engineering relevance are considered: (i) stiffness grading of the bondlayer to enhance performance while retaining the critical length characteristics of bonded anchors and (ii) modulus reduction of the bondlayer representing adhesive degradation proximal to the loaded end. Theoretical solutions are developed adopting a stress function approach in conjunction with a variational method that compare well with 3D axisymmetric Finite Element (FE) results. Both theoretical and FE results indicate that the maximum shear stress in the adhesive decreases over 60% for a graded bondlayer for the parameters considered here without warranting a longer embedment length. In contrast, spatially-stiffness-degraded bondlayer reduces shear stress peaks significantly but warrants a larger embedment length to enable shear-dominated stress-transfer. A design map showing the critical embedment length required for degraded bondlines as a function of fractional embedment length over which bondline is regarded to have degraded is presented. In addition, interfacial fracture behavior of the tailored and degraded adhesive anchors were examined through FE analyses and noted that the tailoring reduces the energy release rate but has the potential for enhancing damage tolerance. The findings of the study indicate that the stiffness-tailored and -degraded bondlines significantly redistribute the stress field with concomitant influence on stress-transfer and interfacial debonding characteristics of bonded anchors

Revolutionizing Renewable Energy Integration: The Innovative Gravity Energy Storage Solution

In recent times, energy storage has been a major concern in the renewable energy sector. Traditional batteries are becoming less effective and sustainable as the world is moving towards renewable energy. Gravity battery, also known as Gravitricity is a new energy storage technology that is gaining popularity in the renewable energy sector. Gravity battery uses excess energy to hoist heavy objects, and when needed, the objects are released, generating energy. This paper highlights the need for alternative energy storage systems and the potential of gravity batteries to address the limitations of traditional batteries. This paper provides an in-depth analysis of gravity battery technology including the need analysis, problem Statement, product producers, advantages, disadvantages, and how it can replace the present batteries in power systems. The paper concludes that gravity battery technology is a promising alternative to traditional batteries and requires further research and development to accelerate its adoption in the renewable energy sector