Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

The role of the Rocky Mountains in shaping the atmospheric mean state and the response to tropical forcing in idealised simulations.

Understanding the natural and forced variability of the atmospheric general circulation and its drivers is one of the grand challenges in climate science. It is of paramount importance to understand to what extent the systematic error of climate models affects the processes driving such variability. This is done by performing a set of simulations (ROCK experiments) with an intermediate complexity atmospheric model (SPEEDY), in which the Rocky Mountains orography is increased or decreased to influence the structure of the North Pacific jet stream. For each of these modified-orography experiments, the climatic response to idealized sea surface temperature anomalies of varying intensity in the El Niño Southern Oscillation (ENSO) region is studied. ROCK experiments are characterized by variations in the Pacific jet stream intensity whose extension encompasses the spread of the systematic error found in Coupled Model Intercomparison Project (CMIP6) models. When forced with ENSO-like idealised anomalies, they exhibit a non-negligible sensitivity in the response pattern over the Pacific North American region, indicating that the model mean state can affect the model response to ENSO. It is found that the classical Rossby wave train response to ENSO is more meridionally oriented when the Pacific jet stream is weaker and more zonally oriented with a stronger jet. Rossby wave linear theory suggests that a stronger jet implies a stronger waveguide, which traps Rossby waves at a lower latitude, favouring a zonal propagation of Rossby waves. The shape of the dynamical response to ENSO affects the ENSO impacts on surface temperature and precipitation over Central and North America. A comparison of the SPEEDY results with CMIP6 models suggests a wider applicability of the results to more resources-demanding climate general circulation models (GCMs), opening up to future works focusing on the relationship between Pacific jet misrepresentation and response to external forcing in fully-fledged GCMs.