How to step by step calculate the thickness of thin plates?4 answersTo calculate the thickness of thin plates, a step-by-step approach can be followed. First, define the calibration thickness of a calibration plate as d0. Measure the thickness d1 of the calibration plate and calculate the difference P1 between d1 and d0. Next, detect the distance A11 to the first surface of the plate and A12 to the second surface using probes. Calculate the thickness D1 of the plate and add the difference P1 to obtain the true thickness of the plate, Z1 = D1 + d1-d0. Another method involves scanning the gap between a rotary shaft and an optical shielding plate to obtain gap information, and then scanning the gap between the optical shielding plate and the thin sheet to obtain second gap information. Process the information to obtain a thickness distribution of the sheet. Additionally, a method using optical beam irradiation and analysis of the reflected signal at three wavelengths can be used to determine the film thickness.
Where are plates applied in structural engineering?3 answersPlates are widely used in various areas of structural engineering, including civil and mechanical engineering fields. They are commonly employed in the construction of buildings, bridges, ships, aerospace structures, and other metal structures. Plates can be made of different materials, such as steel and composite materials. They can be used in different forms, including intact plates, stiffened plates, perforated plates, and stiffened perforated plates. Plates can experience various modes of failure, such as buckling and instability, which need to be analyzed and predicted for their safe design and operation. Overall, plates play a crucial role in the construction and functioning of structures in structural engineering.
What are the mathematical models used to model thin film fluid flow?5 answersMathematical models used to model thin film fluid flow include the homotopy perturbation method combined with Laplace transform and Pade´ approximation approach. Another model is the adaptive fluid modeling framework that uses a traditional 3D Navier-Stokes model for bulk fluid flow and switches to a pseudo 2D thin film flow model when appropriate. The homotopy perturbation method along with Caputo definition of fractional derivative is used to solve modeled fractional-order boundary value problems in thin film flow of non-Newtonian Johnson–Segalman fluid. Additionally, a two-dimensional flow model has been proposed for viscous fluid flow between two close moving surfaces, which converges to the same limit problem as the Navier-Stokes equations depending on the boundary conditions.
What is the formula to shape product?5 answersThe formula for shaping a product involves heating prepregs with reinforcing fibers and a thermoplastic resin, arranging them in layers, and pressing them together to create the desired shape. Another formula is the hook length formula, which gives a product formula for the number of standard Young tableaux of a partition shape. However, not all skew shapes have a product formula for the number of standard Young tableaux. For certain special skew shapes, there is a product formula. Additionally, a product formula has been conjectured for the number of standard Young tableaux of a certain skew shifted shape. These formulas have been proven using Selberg-type integrals.
How to deduce reissner plate theory?5 answersThe Reissner plate theory can be deduced through various mathematical and theoretical approaches. One approach involves studying the convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together, which shows that the Reissner-Mindlin plate model can be derived without the need for a different continuum model or constitutive symmetry hypothesis. Another approach involves considering the kinematic assumptions of the Bolle-Reissner theory and the equilibrium equations in the deformed configuration for the plate, resulting in a system of differential equations applicable to the calculation of stresses in isotropic plates. The asymptotic homogenization method can also be used to derive the equations of the Kirchhoff-Love and Reissner-Mindlin plate theories. Additionally, a variational-asymptotic method can be applied to construct a Reissner-Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions, resulting in an equivalent single-layer Reissner-Mindlin theory with high accuracy.
How do you make thin films?10 answers