A quasi-three-dimensional solution for the bending analysis of simply supported orthotropic piezoelectric shallow shell panels subjected to thermal, mechanical and electrical potential is introduced. The mechanical governing equations are derived in term of three-dimensional equilibrium relations and the classical Maxwell's equations. The trough-the-thickness temperature is modeled by the Fourier's heat conduction equation. The coupled partial differential equations are solved by Navier closed form solutions. The trough-the-thickness profile for electrical potential, temperature profile and displacements is obtained by using a quasi-exact method so-called the differential quadrature method (DQM). Chebyshev polynomials of the third kind are used as the basis functions and the grid thickness domain discretization for the DQM. The interlaminar conditions for transverse stresses, temperature...

Se presenta una solución numérica para el análisis estático tridimensional de láminas graduadas funcionalmente con curvatura constante. La solución se basa en tres ecuaciones de elasticidad escritas en coordenadas curvilíneas ortogonales que son válidas para paneles de cubierta esféricos, cilíndricos y placas rectangulares. Las ecuaciones en términos de las variables de la superficie media se resuelven mediante una suma de armónicos en términos del método de Navier, que es válido solo para estructuras simplemente apoyadas. Las ecuaciones en función de la dirección del espesor se resuelven numéricamente por el método de Cuadratura Diferencial (DQM) que permitió calcular fácilmente la derivada aproximada de una función utilizando una suma ponderada de las funciones evaluadas en una determinada grilla. Las capas de la estructura se discretizan por separado mediante la ...

This paper presents Best Theory Diagrams (BTDs) constructed from non-polynomial terms to identify best shell theories for bending analysis of cross-ply single skin and sandwich shell panels. This structure presents a constant radii of curvature. The shell theories are constructed using Axiomatic/Asymptotic Method (AAM). The different shell theories are described using the Carrera's Unified Formulation. The governing equations are derived from the Principle of Virtual Displacement (PVD). Navier-Type closed form solution is used for solving the bending problem of simply supported doubly curved shell panels subjected to bi-sinusoidal transverse pressure. The BTDs built from non-polynomial functions are compared with Maclaurin expansions. Spherical shell panels with different layer-configurations are investigated. The results demonstrated that the shell models obtained from the BTD using non...

This paper was written in the context of the project: “Desarrollo de materiales avanzados para el diseño de nuevos productos y servicios tecnológicos para la minería Peruana” founded by CONCYTEC (FONDECYT and GRUPO BANCO MUNDIAL) under the contract number N° 032-2019-FONDECYT-BM-INC.INV. The authors of this manuscript appreciate the financial support from the Peruvian Government.

This paper presents an exact solution for doubly-curved shells subjected to thermal loads. The solution is based on equilibrium equations. The through-the-thickness shell temperature is calculated using the Fourier’s heat conduction equation. The governing equations for displacement and temperature are solved using Navier method, which is valid for shell panels with constant curvature and simply-supported edges.

In this paper, a three-dimensional numerical solution for the bending study of laminated composite doubly-curved shells is presented. The partial differential equations are solved analytically by the Navier summation for the midsurface variables; this method is only valid for shells with constant curvature where boundary conditions are considered simply supported. The partial differential equations present different coefficients, which depend on the thickness coordinates. A semi-analytical solution and the so-called Differential Quadrature Method are used to calculate an approximated derivative of a certain function by a weighted summation of the function evaluated in a certain grin domain. Each layer is discretized by a grid point distribution such as: Chebyshev-Gauss-Lobatto, Legendre, Ding and Uniform. As part of the formulation, the inter-laminar continuity conditions of displacement...

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado.

The mechanical behavior of advanced composites can be modeled mathematically through unknown variables and Shear Strain Thickness Functions (SSTFs). Such SSTFs can be of polynomial or non-polynomial nature and some parameters of non-polynomial SSTFs can be optimized to get optimal results. In this paper, these parameters are called “r” and “s” and they are the argument of the trigonometric SSTFs introduced within the Carrera Unified Formulation (CUF). The Equivalent Single Layer (ESL) governing equations are obtained by employing the Principle of Virtual Displacement (PVD) and are solved using Navier method solution. Furthermore, trigonometric expansion with Murakami theory was implemented in order to reproduce the Zig-Zag effects which are important for multilayer structures. Several combinations of optimization parameters are evaluated and selected by different criteria of aver...

The mechanical behavior of advanced composites can be modeled mathematically through unknown variables and Shear Strain Thickness Functions (SSTFs). Such SSTFs can be of polynomial or non-polynomial nature and some parameters of non-polynomial SSTFs can be optimized to get optimal results. In this paper, these parameters are called “r” and “s” and they are the argument of the trigonometric SSTFs introduced within the Carrera Unified Formulation (CUF). The Equivalent Single Layer (ESL) governing equations are obtained by employing the Principle of Virtual Displacement (PVD) and are solved using Navier method solution. Furthermore, trigonometric expansion with Murakami theory was implemented in order to reproduce the Zig-Zag effects which are important for multilayer structures. Several combinations of optimization parameters are evaluated and selected by different criteria of aver...