Modelling methodology of MEMS structures based on Cosserat theory

Modelling MEMS involves a variety of software tools that deal with the analysis of complex geometrical structures and the assessment of various interactions among different energy domains and components. Moreover, the MEMS market is growing very fast, but surprisingly, there is a paucity of modelling and simulation methodology for precise performance verification of MEMS products in the nonlinear regime. For that reason, an efficient and rapid modelling approach is proposed that meets the linear and nonlinear dynamic behaviour of MEMS systems.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

On the basis of the explanation of rotational seismology as an area of study, a modern approach to the seismic rotation in various continuum models is summarized. The aim of this chapter is to formulate the fundamental requirements for rotational seismometer. Consequently, a review of all existing technologies of rotational seismometers including mechanical, electrochemical, magnetohydrodynamical, as well as optical type solutions is discussed. The analysis of their parameters that considers technical requirements enforced by rotational seismology has indicated an optical instrument using a Sagnac interferometer as the best solution. Fibre-Optic System for Rotational Events & phenomena Monitoring (FOSREM) with its main parameters and features is described as an example of such solution. Moreover, the example of rotational events recorded in Książ observatory, Poland, using mechanical rotational seismometers and FOSREM is presented. There are data for M = 3.8 earthquake near Jarocin, Poland on the 2012.01.06 at 15:37:56 at a distance of about 200 km from Książ. Although the used devices have totally different designs, the results obtained using FOSREM and the results calculated by mechanical devices show compatibility in rotational signals

Design and Modeling of Multi-Arm Continuum Robots

Continuum robots are snake-like systems able to deliver optimal therapies to pathologies deep inside the human cavity by following 3D complex paths. They show promise when anatomical pathways need to be traversed thanks to their enhanced flexibility and dexterity and show advantages when deployed in the field of single-port surgery. This PhD thesis concerns the development and modelling of multi-arm and hybrid continuum robots for medical interventions. The flexibility and steerability of the robot’s end-effector are achieved through concentric tube technology and push/pull technology. Medical robotic prototypes have been designed as proof of concepts and testbeds of the proposed theoretical works.System design considers the limitations and constraints that occur in the surgical procedures for which the systems were proposed for. Specifically, two surgical applications are considered. Our first prototype was designed to deliver multiple tools to the eye cavity for deep orbital interventions focusing on a currently invasive intervention named Optic Nerve Sheath Fenestration (ONSF). This thesis presents the end-to-end design, engineering and modelling of the prototype. The developed prototype is the first suggested system to tackle the challenges (limited workspace, need for enhanced flexibility and dexterity, danger for harming tissue with rigid instruments, extensive manipulation of the eye) arising in ONSF. It was designed taking into account the clinical requirements and constraints while theoretical works employing the Cosserat rod theory predict the shape of the continuum end-effector. Experimental runs including ex vivo experimental evaluations, mock-up surgical scenarios and tests with and without loading conditions prove the concept of accessing the eye cavity. Moreover, a continuum robot for thoracic interventions employing push/pull technology was designed and manufactured. The developed system can reach deep seated pathologies in the lungs and access regions in the bronchial tree that are inaccessible with rigid and straight instruments either robotically or manually actuated. A geometrically exact model of the robot that considers both the geometry of the robot and mechanical properties of the backbones is presented. It can predict the shape of the bronchoscope without the constant curvature assumption. The proposed model can also predict the robot shape and micro-scale movements accurately in contrast to the classic geometric model which provides an accurate description of the robot’s differential kinematics for large scale movements

On a family of numerical models for couple stress based flexoelectricity for continua and beams

A family of numerical models for the phenomenological linear flexoelectric theory for continua and their particularisation to the case of three-dimensional beams based on a skew-symmetric couple stress theory is presented. In contrast to the standard strain gradient flexoelectric models which assume coupling between electric polarisation and strain gradients, we postulate an electric enthalpy in terms of linear invariants of curvature and electric field. This is achieved by introducing the axial (mean) curvature vector as a strain gradient measure. The physical implication of this assumption is many-fold. Firstly, analogous to the standard strain gradient models, for isotropic (non-piezoelectric) materials it allows constructing flexoelectric energies without breaking material’s centrosymmetry. Secondly, unlike the standard strain gradient models, nonuniform distribution of volumetric part of strains (volumetric strain gradients) do not generate electric polarisation, as also confirmed by experimental evidence to be the case for some important classes of flexoelectric materials. Thirdly, a state of plane strain generates out of plane deformation through strain gradient effects. Finally, under this theory, extension and shear coupling modes cannot be characterised individually as they contribute to the generation of electric polarisation as a whole. As a first step, a detailed comparison of the developed couple stress based flexoelectric model with the standard strain gradient flexoelectric models is performed for the case of Barium Titanate where a myriad of simple analytical solutions are assumed in order to quantitatively describe the similarities and dissimilarities in effective electromechanical coupling under these two theories. From a physical point of view, the most notable insight gained is that, if the same experimental flexoelectric constants are fitted in to both theories, the presented theory in general, reports up to 200% stronger electromechanical conversion efficiency. From the formulation point of a view, the presented flexoelectric model is also competitively simpler as it eliminates the need for high order strain gradient and coupling tensors and can be characterised by a single flexoelectric coefficient. In addition, three distinct mixed flexoelectric variational principles are presented for both continuum and beam models that facilitate incorporation of strain gradient measures in to a standard finite element scheme while maintaining the C0 continuity. Consequently, a series of low and high order mixed finite element schemes for couple stress based flexoelectricity are presented and thoroughly benchmarked against available closed form solutions in regards to electromechanical coupling efficiency. Finally, nanocompression of a complex flexoelectric conical pyramid for which analytical solution cannot be established is numerically studied where curvature induced necking of the specimen and vorticity around the frustum generate moderate electric polarisation

Computational homogenization for the multi-scale analysis of multi-phase materials

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Dynamic structural analysis of beams

The research reviews the various methods, accurate and approximate, analytical and numerical, used for the analysis of beams that are subjected to dynamic loads. A review of previous research is presented. A detailed description of one of the methods, the Simplified Elastic Plastic Method (the SEP Method), a well-developed approximate method, is given. A finite element model, built with the aid of the computer software ABAQUS, is described. Results of 20 experiments made by others are provided and used as a benchmark for the finite element analysis. The methodology used for the validation of the ABAQUS Model and the SEP Method is to do, for various study cases, a comparison between the experimental results, those computed using the ABAQUS Model and those predicted using the SEP Method. Having validated the ABAQUS Model, it has been used as a benchmark with which to check the SEP Method. Therefore, additional cases have been analysed using the ABAQUS Model in order to cover a more comprehensive range of variables. A good agreement has been found between the results. The accuracy of the ABAQUS model and the conservatism of the SEP Method are shown. A design procedure using the SEP Method has been developed. Calibration factors are also proposed in order to reduce the conservatism in the SEP Method. The results and recommendations of the research can be employed in the defence industry, civil and structural engineering

Thermal analysis of wood-steel hybrid construction

Main goal of this work is to present a numerical model to study the thermal necrosis due a dental drilling process, with and without water irrigation. Also an experimental methodology is used to measure the thermal occurrence in a pig mandible. Motivation, the assessment of bone damage, using the temperature criterion (above 55ºC

A numerical method for fluid-structure interactions of slender rods in turbulent flow

This thesis presents a numerical method for the simulation of fluid-structure interaction (FSI) problems on high-performance computers. The proposed method is specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic structures, the latter being modeled as Cosserat rods. From a numerical point of view, such kind of FSI requires special techniques to reach numerical stability. When using a partitioned fluid-structure coupling approach this is usually achieved by an iterative procedure, which drastically increases the computational effort. In the present work, an alternative coupling approach is developed based on an immersed boundary method (IBM). It is unconditionally stable and exempt from any global iteration between the fluid part and the structure part. The proposed FSI solver is employed to simulate the flow over a dense layer of vegetation elements, usually designated as canopy flow. The abstracted canopy model used in the simulation consists of 800 strip-shaped blades, which is the largest canopy-resolving simulation of this type done so far. To gain a deeper understanding of the physics of aquatic canopy flows the simulation data obtained are analyzed, e.g., concerning the existence and shape of coherent structures

A numerical and analytical study of size effects in free vibration of heterogeneous materials

In this thesis, the influence of the periodic microstructure on the dynamic mechanical behaviour of geometrically similar heterogeneous samples, namely 2D beams and 3D plates, with different dimensions and boundary textures but constant aspect ratio has been numerically investigated. Beam samples of a representative material comprised of 2D unit-cells were created using the conventional finite element analysis (FEA) to identify and quantify size effects existing in flexural modal frequencies when the scale of microstructure becomes comparable to the macroscopic dimensions. The unit cells were created so as to keep the overall properties of the material at the macroscopic scale constant despite variations in the void or inclusions volume fraction. The finite element numerical results were then compared against the analytical results obtained from the enhanced nonlocal Timoshenko beam which incorporates the Eringen small length scale coefficients, but the values obtained for the coefficient exhibited size dependency. Accordingly, 2D analysis using a novel finite element method (MPFEM) or, alternatively, the control volume based finite element method (CVFEM) was carried out by incorporating micropolar constitutive behaviour into their formulation. The numerical predictions using either MPFEM or CVFEM were then matched with the FEA results to obtain additional constitutive parameters featuring in planar micropolar elasticity theory. The 2D models were then extruded to form square 3D plates as a straightforward progression. These samples demonstrated a moderate degree of anisotropy, which increased with volume fraction. Nevertheless, the 3D-MPFEM models which assume isotropy agreed with the dynamic behaviour of FEA nonhomogeneous models with low volume fractions, which were mildly anisotropic. Subsequently, to reduce the anisotropy, 3D square plate samples with a square-pyramidal geometry, or a body-centred cubic, arrangement of spherical voids and inclusions were modelled which demonstrated approximately isotropic characteristics for which the 3D-MPFEM results agreed with the finite element results at lower mode numbers.In this thesis, the influence of the periodic microstructure on the dynamic mechanical behaviour of geometrically similar heterogeneous samples, namely 2D beams and 3D plates, with different dimensions and boundary textures but constant aspect ratio has been numerically investigated. Beam samples of a representative material comprised of 2D unit-cells were created using the conventional finite element analysis (FEA) to identify and quantify size effects existing in flexural modal frequencies when the scale of microstructure becomes comparable to the macroscopic dimensions. The unit cells were created so as to keep the overall properties of the material at the macroscopic scale constant despite variations in the void or inclusions volume fraction. The finite element numerical results were then compared against the analytical results obtained from the enhanced nonlocal Timoshenko beam which incorporates the Eringen small length scale coefficients, but the values obtained for the coefficient exhibited size dependency. Accordingly, 2D analysis using a novel finite element method (MPFEM) or, alternatively, the control volume based finite element method (CVFEM) was carried out by incorporating micropolar constitutive behaviour into their formulation. The numerical predictions using either MPFEM or CVFEM were then matched with the FEA results to obtain additional constitutive parameters featuring in planar micropolar elasticity theory. The 2D models were then extruded to form square 3D plates as a straightforward progression. These samples demonstrated a moderate degree of anisotropy, which increased with volume fraction. Nevertheless, the 3D-MPFEM models which assume isotropy agreed with the dynamic behaviour of FEA nonhomogeneous models with low volume fractions, which were mildly anisotropic. Subsequently, to reduce the anisotropy, 3D square plate samples with a square-pyramidal geometry, or a body-centred cubic, arrangement of spherical voids and inclusions were modelled which demonstrated approximately isotropic characteristics for which the 3D-MPFEM results agreed with the finite element results at lower mode numbers