This article presents a new kind of higher-order deformation theory, called Parametric Higher-order Deformation Theory (PHDT), for the static analysis of functionally graded plates (FGPs). The novelty of the PHDT is the use of strain shape functions that are calibrated by a set of tuning parameters to approximate 3D results along the plate thickness. The tuning parameters are assumed to vary with side-to-thickness ratios and power-law indexes. In contrast to higher-order shear deformation theories (HSDTs), the PHDT is not mathematically constrained to satisfy the traction-free boundary condition on the bottom plate’s surface. The proposed plate model is based on a 5-unknown HSDT previously presented by one of the authors. The governing equations are derived from the principle of virtual works, and Navier-type closed form solutions have been obtained for simply supported FGPs subjected ...

This paper presents a static analysis of functionally graded single and sandwich beams by using an efficient 7DOFs quasi-3D hybrid type theory. The governing equations are derived by employing the principle of virtual works in a weak form and solved by means of the Finite Element Method (FEM). A C1 cubic Hermite interpolation is used for the vertical deflection variables while C0 linear interpolation is employed for the other kinematics variables. Convergence rates are studied in order to validate the finite element technique. Numerical results of the present formulation are compared with analytical and FEM solutions available in the literature.

This paper presents a static analysis of functionally graded (FG) single and sandwich beams by using a simple and efficient 4-unknown quasi-3D hybrid type theory, which includes both shear deformation and thickness stretching effects. The governing equations and boundary conditions are derived by employing the principle of virtual works. Navier-type closed-form solution is obtained for several beams. New hybrid type shear strain shape functions for the inplane and transverse displacement were introduced in general manner to model the displacement field of beams. Numerical results of the present compact quasi-3D theory are compared with other quasi-3D higher order shear deformation theories (HSDTs).

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is subjected to different mechanical loads, specifically: bi-sinusoidal, uniform, patch, hydrostatic pressure and point load. The governing equations are derived from the Principle of Virtual displacement and solved via Navier-Type closed form solutions. The results are compared with results from Layer-wise solutions and different higher order shear deformation theories available. It is shown that refined models with non-polynomial terms are able to accurately predict the through-the-thickness displaceme...

This study presents a static analysis of laminated composite doubly curved shells using a refined kinematic model with polynomial and non-polynomial functions. In particular Maclaurin, trigonometric, exponential and zig-zag functions are employed. Refined models are based on the Equivalent Single Layer theories and obtained by using Carrera Unified formulation. The shell model is subjected to different mechanical loading such as bi-sinusoidal, uniform and point load. The governing equations are derived from the principle of virtual displacement and solved via Navier-Type closed form solutions. The results are compared with Layer-wise and higher-order shear deformation solutions available in the literature. It is shown that refined models with non-polynomial terms are capable of accurately predicting the through-the-thickness displacements and stress distributions with a low computational...

Simulations that calculate the breakage of a given material allow for estimating the particle size produced by comminution equipment. However, conducting these simulations requires a significant amount of time and incurs high computational costs due to the progressive increase in the number of particles during the breakage events. This challenge has prompted the exploration of alternatives, such as employing impact energies present in simulations with solid particles. This study examines the application of two breakage models to particle speeds, analyzing the correlation between the t10 value obtained from simulations using solid particles and the value obtained when simulations include breakage. The findings reveal a linear relationship between the results obtained from simulations with breakage and those with solid particles for a rotor that primarily impacts particles during their ini...