Theoretical and Numerical Analysis of deformation in fixture body plates

A fixture body consists of the base, second, and third plates, which are connected perpendicular to each other. The design of these plates is conducted based on the amount of their elastic deformation under the applied loads. Modeling of deformation in these plates is done specifically for each plate due to their different boundary and loading conditions. In the present study, two distinct analytical models are presented based on the theory of plates and shells to calculate the elastic deformation in the base, second, and third plates of the fixture body. Navier’s method (double series solution) was used to calculate the base plate deformation, in which the plate deformation was modeled by Fourier series, the coefficients of which were calculated based on the intensity and position of the external forces and moments. The deformations of the second and third plates were calculated by developing the differential equation governing the problem using Lagrange’s theory and applying loading and boundary conditions to it. Numerical analysis was conducted in the finite element analysis software to validate the theoretical predictions. The maximum elastic deformation of the base plate was obtained as 2.021 mm from the simulation, showing the maximum error of 4.7% in the theoretical predictions. Also, the maximum elastic deformation for the second and third plates was calculated as 0.0412 mm and 0.0391 mm from the numerical analysis, respectively. It can be concluded that the maximum error in theoretical predictions of deformation in the second and third plates was equal to 1.4%.