Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .

Thermochemical characterisation of Parinari polyandra Benth fruit shell

The aim of this work is to investigate the thermochemical characteristics of Parinari polyandra Benth fruit shell. An agricultural waste residue is investigated using standard methods including thermogravimetric analysis (TGA), proximate and ultimate analysis, structural composition and bomb calorimeter. The proximate and ultimate analyses were carried out to determine the ash and fixed carbon contents, volatile matter, and elemental compositions. The structural composition analysis determined the hemicellulose, cellulose, and lignin content of the biomass. The measured calorific value obtained was 20.5. MJ/kg. The TGA and DTG profiles indicate the waste fruit shells are viable for pyrolysis reaction. The inorganic contents are relatively low with potassium found to be the most abundant element. The hemicelluloses and cellulose contents are indicative of relatively higher rate of pyrolysis and comparable with established biomass utilised for bio-oil production.

An improved static model for tool deflection in machining of Ti–6Al–4V acetabular shell produced by selective laser melting

Tool deflection during milling operation leads to dimensional error, decreasing surface quality and increasing rejection rate. In this study, tool deflection during the milling of the inner surfaces of Ti–6Al–4V prosthetic acetabular shell produced by selective laser melting (SLM) was modelled. The first purpose of this research is to provide a general static cutting tool deflection model for ball nose cutters where deviation of machine components and tool holder are so small as to be considered negligible. This is because the values of machine component and tool holder deflection were lower than standard tolerances (10 μm) and found to be lower than 1/15 of tool deflection. The second and third objectives of this work involve calculating contact surfaces by determining workpiece and tool geometry and choosing second moment of inertia using a novel cross section method (CSM). Static models for three quasi-analytical methods (QAM) that are simple cantilever beam model (SCBM), two-section model (TWSM) and our three section model (THSM) are presented. THSM showed high accuracy which was validated by 3D finite element method (FEM3D) and experimental measurements. The accuracy of tool deflection calculation using THSM by computing, shank, flute and ball head deflection and also utilizing CSM to determine second moment of inertia showed notable improvements.

Phase-field analysis of finite-strain plates and shells including element subdivision

With the theme of fracture of finite-strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase- field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics

In this study, a finite element (FE) framework for the analysis of the interplay between buckling and delamination of thin layers bonded to soft substrates is proposed. The current framework incorporates the following modeling features: (i) geometrically nonlinear solid shell elements, (ii) geometrically nonlinear cohesive interface elements, and (iii) hyperelastic material constitutive response for the bodies that compose the system. A fully implicit Newton–Raphson solution strategy is adopted to deal with the complex simultaneous presence of geometrical and material nonlinearities through the derivation of the consistent FE formulation. Applications to a rubber-like bi-material system under finite bending and to patterned stiff islands resting on soft substrate for stretchable solar cells subjected to tensile loading are proposed. The results obtained are in good agreement with benchmark results available in the literature, confirming the accuracy and the capabilities of the proposed numerical method for the analysis of complex three-dimensional fracture mechanics problems under finite deformations.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.