El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / 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 displacements and transverse shear stresses between the interfaces of two layers are imposed. The proper traction conditions at the top and bottom of the shell due to applied transverse loadings are also considered. The present results are compared with other 3D solutions available in the literature, classical 2D models, Layer-wise models, etc. Comparison of the results show that the present formulation correctly predicts through-the-thickness distributions for stresses and displacements while maintaining a low computational cost. / Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / In this paper, a three-dimensional bending solution of doubly-curved shells subjected to mechanical, thermal and hygrothermal load is studied. Through-the-thickness temperature of the shell is modeled by Fourier's heat conduction equation. Fick's moisture diffusion law equation is used to determine the hygro-thermal profile through-the-thickness. The partial differential equations are solved by using the Navier closed form summations which are valid only for shells with constant radii of curvature among the midsurface and with simply supported boundary conditions on its shell's edges. The shell governing equations are solved by discretizing the thickness profile via Legendre's grid distribution and by using the Differential Quadrature Method (DQM). The Layerwise capabilities of the method is guaranteed by imposing the inter-laminar continuity of out-of-the-plane stresses, displacements, temperature and hygrothermal load thickness profile. The zero-stress condition for the transverse shear stresses is imposed due to the fact that no mechanical loads are applied in those directions. Results for cylindrical, spherical panels and rectangular plates are presented. Comparisons are made with Layerwise and three-dimensional solutions available in literature. The results have strong accuracy and a benchmark problem is delivered. / Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica

The response of cucumber (Cucumis sativus L.) plants to various root and shoot environments (solution depth, temperature, ionic strength, nitrogen and calcium level and light intensity) were studied. Cucumber plants were grown in continuously circulating-solution in a heated-glasshouse. Dry weights of leaves, stems and roots, leaf area, leaf number, root length and root number were measured as well as uptake of potassium, calcium and nitrogen. The relationship between shoot and root in terms of functional equilibrium equations was also examined. The results presented show that: 1. Shoot growth of cucumber plants was reduced if grown in solutions of less than 50mm in depth; 2. When roots were grown in shallow solution depths at 1 or 5mm the dry weight allocated to the root increased. The ratio of root number/root length(no./cm) also increased. Lowering solution temperature to 12.5±2.5°C enhanced the production of root number relctive to root length, and 5 and 2% of full strength and 5% of full strength nitrogen level solution stimulated the growth of root length relative to root number; 3. Under low solution temperature treatment leaf number was maintained at the expense of leaf area. Under low total ionic strength and low nitrogen solution, enhanced root length growth was at the expense of leaf area growth; 4. Low solution temperature enhanced the dry weight allocated to the stem relative to the leaf. Low total ionic strength and low nitrogen solution increased the dry weight allocated to the leaf relative to the stem; 5. The specific activity of root, represented by specific absorption rate, increased when the shoot was under light stress and, the specific activity of shoot, represented by unit shoot rate, increased when the root was under nitrogen-stress; 6. The form of equation developed by Thornley (ΔM = fmΔW, where ΔM is the increment in weight of element M and ΔW the increment in total plant dry weight during a time period Δt with fm a constant) showed a better relationship than the equation developed by Davidson [root mass x rate(absorption) ∝ leaf mass x rate(photosynthesis)] and subsequently used by Hunt in the form of mass ratio(root/shoot) ∝ l/activity ratio; 7. The equation developed by Chung et al, total plant weight/(leaf number/leaf area) ∝ total "k"/(root number/root length), where k represents the total contents of elements or compounds, showed a good approximation of the relationship between shoot and root under all the environmental stresses imposed with the exception of calcium uptake. The results support the concept that the activity of the root or shoot in carrying out its function is influenced by the demand created by the opposite organ and appears to be a better assumption than that which proposes that the activity of an organ is solely dependent on its own size.

The response of cucumber (Cucumis sativus L.) plants to various root and shoot environments (solution depth, temperature, ionic strength, nitrogen and calcium level and light intensity) were studied. Cucumber plants were grown in continuously circulating-solution in a heated-glasshouse. Dry weights of leaves, stems and roots, leaf area, leaf number, root length and root number were measured as well as uptake of potassium, calcium and nitrogen. The relationship between shoot and root in terms of functional equilibrium equations was also examined. The results presented show that: 1. Shoot growth of cucumber plants was reduced if grown in solutions of less than 50mm in depth; 2. When roots were grown in shallow solution depths at 1 or 5mm the dry weight allocated to the root increased. The ratio of root number/root length(no./cm) also increased. Lowering solution temperature to 12.5±2.5°C enhanced the production of root number relctive to root length, and 5 and 2% of full strength and 5% of full strength nitrogen level solution stimulated the growth of root length relative to root number; 3. Under low solution temperature treatment leaf number was maintained at the expense of leaf area. Under low total ionic strength and low nitrogen solution, enhanced root length growth was at the expense of leaf area growth; 4. Low solution temperature enhanced the dry weight allocated to the stem relative to the leaf. Low total ionic strength and low nitrogen solution increased the dry weight allocated to the leaf relative to the stem; 5. The specific activity of root, represented by specific absorption rate, increased when the shoot was under light stress and, the specific activity of shoot, represented by unit shoot rate, increased when the root was under nitrogen-stress; 6. The form of equation developed by Thornley (∆M = fm∆W, where ∆M is the increment in weight of element M and ∆W the increment in total plant dry weight during a time period ∆t with fm a constant) showed a better relationship than the equation developed by Davidson [root mass x rate(absorption) ∝ leaf mass x rate(photosynthesis)] and subsequently used by Hunt in the form of mass ratio(root/shoot) ∝ l/activity ratio; 7. The equation developed by Chung et al, total plant weight/(leaf number/leaf area) ∝ total "k"/(root number/root length), where k represents the total contents of elements or compounds, showed a good approximation of the relationship between shoot and root under all the environmental stresses imposed with the exception of calcium uptake. The results support the concept that the activity of the root or shoot in carrying out its function is influenced by the demand created by the opposite organ and appears to be a better assumption than that which proposes that the activity of an organ is solely dependent on its own size.