Coupled model for the non-linear analysis of anisotropic sections subjected to general 3D loading. Part 1: Theoretical formulation

A numerical model for the coupled analysis of arbitrary shaped cross sections made of heterogeneous-anisotropic materials under 3D combined loading is formulated. The theory is derived entirely from equilibrium considerations and based on the superposition of the 3D section’s distortion and the traditional plane section hypothesis. 3D stresses and strains fields are obtained as well as a section stiffness matrix reflecting coupling effects between normal and tangential forces due to material anisotropy. Traditional generalized strains and stresses are maintained as input and output variables. The proposed model is suitable as a constitutive law for frame elements in the analysis of complete structures.     

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: Bending and free vibrations

This paper addresses the bending and free vibrations of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation

In the nonlinear analysis of elastic structures, the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations. Based on the updated Lagrangian (UL) formulation, the geometric stiffness matrix [k_g] is derived for a 3D rigid beam element from the virtual work equation using a rigid displacement field. Further, by treating the three-node triangular plate element (TPE) as the composition of three rigid beams lying along the three sides, the [k_g] matrix for the TPE can be assembled from those of the rigid beams. The idea for the UL-type incremental-iterative nonlinear analysis is that if the rigid rotation effects are fully taken into account at each stage of analysis, then the remaining effects of natural deformations can be treated using the small-deformation linearized theory. The present approach is featured by the fact that the formulation is simple, the expressions are explicit, and all kinds of actions are considered in the stiffness matrices. The robustness of the procedure is demonstrated in the solution of several benchmark problems involving the postbuckling response.     

Building a geodatabase for mapping hydrogeological features and 3D modeling of groundwater systems: Application to the Saguenay-Lac-St.-Jean region, Canada

Understanding and managing groundwater resources require the integration of a large amount of high-quality data from a variety of sources. Due to the limitations in accessing information related to groundwater and subsurface conditions, the gathering of available existing information is of crucial importance when conducting a successful hydrogeological study. Here, we present an approach for the development of an exhaustive and comprehensive groundwater database through (1) the gathering of relevant sources of information relating to groundwater, and (2) the application of a quality control process in order to screen the data for accuracy and quality. This hydrogeological database is then implemented within a GIS (geographic information system) framework coupled to a Relational Database Management System (RDBMS) as a personal geodatabase (ESRI format) GIS technology. Once established, the spatial database allows a user to request the relevant data required for a specific hydrogeological study. In addition, stratigraphic data stored within the spatial database may be utilized for constructing 3D subsurface hydrostructural models. In order to achieve this objective, the software Arc Hydro Groundwater combined with the ArcGIS spatial database is shown to be appropriate for the 3D structural representation of aquifers (groundwater reservoirs). The innovative contribution of this approach in building 3D hydrostructural subsurface models from a spatial database resides in simplifying the required step-by-step processes by considering a unified compatible combination of “RDBMS-ArcGIS-Arc Hydro Groundwater” technologies. The proposed methodology is illustrated using data from an ongoing project aimed at developing an inventory of the groundwater resources of the Saguenay-Lac-Saint-Jean region, Quebec (Canada).     

Gibbs2: A new version of the quasiharmonic model code. II. Models for solid-state thermodynamics, features and implementation

In the second article of the series, we present the Gibbs2 code, a Fortran90 reimplementation of the original Gibbs program [Comput. Phys. Commun. 158 (2004) 57] for the calculation of pressure–temperature dependent thermodynamic properties of solids under the quasiharmonic approximation. We have taken advantage of the detailed analysis carried out in the first paper to implement robust fitting techniques. In addition, new models to introduce temperature effects have been incorporated, from the simple Debye model contained in the original article to a full quasiharmonic model that requires the phonon density of states at each calculated volume. Other interesting novel features include the empirical energy corrections, that rectify systematic errors in the calculation of equilibrium volumes caused by the choice of the exchange-correlation functional, the electronic contributions to the free energy and the automatic computation of phase diagrams. Full documentation in the form of a user?s guide and a complete set of tests and sample data are provided along with the source code.

Program summary

Program title:Gibbs2Catalogue identifier: AEJI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, v3No. of lines in distributed program, including test data, etc.: 936 087No. of bytes in distributed program, including test data, etc.: 8 596 671Distribution format: tar.gzProgramming language: Fortran90Computer: Any running Unix/LinuxOperating system: Unix, GNU/LinuxClassification: 7.8External routines: Part of the minpack, pppack and slatec libraries (downloaded from www.netlib.org) are distributed along with the program.Nature of problem: Given the static E(V) curve, and possibly vibrational information such as the phonon density of states, calculate the equilibrium volume and thermodynamic properties of a solid at arbitrary temperatures and pressures in the framework of the quasiharmonic approximation.Additional comments: A detailed analysis concerning the fitting of equations of state has been carried out in the first part of this article, and implemented in the code presented here.Running time: The tests provided only take a few seconds to run.     

Study of the Radio Frequency (RF) performance of a Wafer-Level Package (WLP) with Through Silicon Vias (TSVs) for the integration of RF-MEMS and micromachined waveguides in the context of 5G and Internet of Things (IoT) applications. Part 2: parameterised 3D model and optimisation

Microsystem Technologies - This study discusses the exploitation of a full-3D methodology for the electromagnetic simulation of a Wafer-Level Packaging solution featuring Through Silicon Vias...