This is a “cheat sheet”, which means that it consists of information packaged in a concise and efficient way so that it can easily be used as a quick reference. The topic is ranks of elliptic curves, mostly over Q. This is a slightly revised version of the handout I wrote as a supplement to my survey talk “Distributions of Ranks of Elliptic Curves” at MSRI’s Connections for Women: Arithmetic St...

Composite sandwich structural joints, such as T-joints, are used in many different composite applications to transfers the load orthogonally between two sandwich elements. However, these joints connecting the sections can represent the weakest link in sandwich composite structures due to the lack of reinforcement in the out-of-plane direction. Therefore, this paper presents a new methodology fo...

In a Z-core sandwich panel, the shear stiffness of the sandwich panel in the weak direction which is perpendicular to the placement of the Z-cores is much smaller than the bending stiffness because the hollow section between the two facing plates cannot sustain shear action. Because of this fact, the shear deformation of a Z-core sandwich panel under bending in the weak direction cannot be igno...

The main aim of this paper is to investigate bending behavior in sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is devel...

In this paper, a new roofing system is introduced, which is constructued using the precast composite sandwich panels. This roofing sandwich panels system consists of three kinds of precast concrete sandwich panels including capital panels, beam or between columns panels, and slab or middle panels. The panels are composed of three layers; A high strength reinforced concrete top layer. A thick la...

In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satis...

The present article investigates the thermoelastic interaction in a three-dimensional homogeneous and isotropic sandwich structure using the dual-phase-lag (DPL) model of generalized thermoelasticity. The incorporated resulting non-dimensional coupled equations are applied to a specific problem in which a sandwich layer of unidentical homogeneous and isotropic substances is subjected to time-de...

Twenty-three percent of carbon emissions come from fossil fuels used in transportation. Electric vehicles are suggested as alternatives to fossil-fueled vehicles. Cars having vehicle integrated photovoltaics (VIPV) on the roof have recently been launched, aiming increase fuel efficiency and maximum mileage by supplying electricity when needed. VIPV needs be light terms efficiency. The use polym...

As I take the queuing system course, I become interested in the queuing systems in our life, for example, the cafeteria in the school. In this project, I want to model an interesting queuing system I observed in some cafeteria on campus, and study the behaviour and performance of the queuing system at the cafeteria. When I go to the Jazz Café in Darrin Communications Center, I noticed that ther...

In this paper, the vibrational and buckling analysis of a cylindrical sandwich panel with an elastic core under thermo-mechanical loadings is investigated. The modeled cylindrical sandwich panel as well as its equations of motions and boundary conditions is derived by Hamilton’s principle and the first-order shear deformation theory (FSDT). For the first time in the present study, various bound...