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.

Fault delineation and stress orientations from the analysis of background, low magnitude seismicity in Southern Apennines (Italy)

The aim of this work was to show that refined analyses of background, low magnitude seismicity allow to delineate the main active faults and to accurately estimate the directions of the regional tectonic stress that characterize the Southern Apennines (Italy), a structurally complex area with high seismic potential. Thanks the presence in the area of an integrated dense and wide dynamic network, was possible to analyzed an high quality microearthquake data-set consisting of 1312 events that occurred from August 2005 to April 2011 by integrating the data recorded at 42 seismic stations of various networks. The refined seismicity location and focal mechanisms well delineate a system of NW-SE striking normal faults along the Apenninic chain and an approximately E-W oriented, strike-slip fault, transversely cutting the belt. The seismicity along the chain does not occur on a single fault but in a volume, delimited by the faults activated during the 1980 Irpinia M 6.9 earthquake, on sub-parallel predominant normal faults. Results show that the recent low magnitude earthquakes belongs to the background seismicity and they are likely generated along the major fault segments activated during the most recent earthquakes, suggesting that they are still active today thirty years after the mainshock occurrences. In this sense, this study gives a new perspective to the application of the high quality records of low magnitude background seismicity for the identification and characterization of active fault systems. The analysis of the stress tensor inversion provides two equivalent models to explain the microearthquake generation along both the NW-SE striking normal faults and the E- W oriented fault with a dominant dextral strike-slip motion, but having different geological interpretations. We suggest that the NW-SE-striking Africa-Eurasia convergence acts in the background of all these structures, playing a primary and unifying role in the seismotectonics of the whole region.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.

A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

Seismic sequences analysis for estimation of earthquake source parameters: corner frequency, stress drop, and seismic moment observations

The present study has been carried out with the following objectives: i) To investigate the attributes of source parameters of local and regional earthquakes; ii) To estimate, as accurately as possible, M0, fc, Δσ and their standard errors to infer their relationship with source size; iii) To quantify high-frequency earthquake ground motion and to study the source scaling. This work is based on observational data of micro, small and moderate -earthquakes for three selected seismic sequences, namely Parkfield (CA, USA), Maule (Chile) and Ferrara (Italy). For the Parkfield seismic sequence (CA), a data set of 757 (42 clusters) repeating micro-earthquakes (0 ≤ MW ≤ 2), collected using borehole High Resolution Seismic Network (HRSN), have been analyzed and interpreted. We used the coda methodology to compute spectral ratios to obtain accurate values of fc , Δσ, and M0 for three target clusters (San Francisco, Los Angeles, and Hawaii) of our data. We also performed a general regression on peak ground velocities to obtain reliable seismic spectra of all earthquakes. For the Maule seismic sequence, a data set of 172 aftershocks of the 2010 MW 8.8 earthquake (3.7 ≤ MW ≤ 6.2), recorded by more than 100 temporary broadband stations, have been analyzed and interpreted to quantify high-frequency earthquake ground motion in this subduction zone. We completely calibrated the excitation and attenuation of the ground motion in Central Chile. For the Ferrara sequence, we calculated moment tensor solutions for 20 events from MW 5.63 (the largest main event occurred on May 20 2012), down to MW 3.2 by a 1-D velocity model for the crust beneath the Pianura Padana, using all the geophysical and geological information available for the area. The PADANIA model allowed a numerical study on the characteristics of the ground motion in the thick sediments of the flood plain.