Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain. Three major problems have been addressed: • Homogenization and analysis of RVE without any defects • Homogenization and analysis of RVE with fiber-matrix de-bonding • Homogenization and analysis of RVE with radial matrix cracking. Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems analytically. The results have been compared against standard results in the literature and against 3D FEA. At the end, results for “Radial deformation due to torsion” problem will be presented which was solved “accidentally.”

Quick and accurate predictions of equivalent properties for thin-walled composite structures are required in the preliminary design process. Existing literature provides analytical solutions to some structures but is limited to particular cases. No unified approach exists to tackle homogenization of thin-walled structures such as beams, plates, or three-dimensional structures using the thin-walled approximation. In this work, a unified approach is proposed to obtain equivalent properties for beams, plates, and three-dimensional structures for thin-walled composite structures using mechanics of structure genome. The adopted homogenization technique interprets the unit cell associated with the composite structures as an assembly of plates, and the overall strain energy density of the unit cell as a summation of the plate strain energies of these individual plates. The variational asymptotic method is then applied to drop all higher-order terms and the remaining energy is minimized with respect to the unknown fluctuating functions. This has been done by discretizing the two-dimensional unit cell into one-dimensional frame elements in a finite element description. This allows the handling of structures with different levels of complexities and internal geometry within a general framework. Comparisons have been made with other works to show the advantages which the proposed model offers over other methods.

The aim of this investigation was to review literature for the most suitable aeroelastic tailoring analysis tools for long slender composite structures, and integrate them into an aeroelastic tailoring process. The JS1C Revelation is a high performance sailplane made from modern composites, mostly carbon fibre. This has the advantage of being more rigid than traditional engineering materials, thereby reducing the effects of the twisting deflections on these long slender structures due to aerodynamic loads. The implementing of aeroelastic tailoring can create bend-twist couples for performance improvements. Composites enable the use of aeroelastic tailoring to improve gliding performance. Flaperon 3 of the JS1C 21 m was used as the design problem for aeroelastic tailoring. Aeroelastic tailoring was done by analysing the flaperon structure at the different layup angles to determine the correct design point to tailor the structure to improve aerodynamic performance at thermalling and cruise, but mostly cruise since it accounts for 70% of the flight time. The composite structure analysis tool has the objective to get results during concept design. This directed the line of research of analysis tools to a solution method of two dimensional cross-section mesh properties projected onto a one dimensional beam. The literature of Hodges had good verification and published data on the analysis tools. The analysis tools comprised of three programs that were not very user friendly. Thus the author compiled a Matlab program as a user interface tool to run the three programs together. The aeroelastic tailoring process systematically works through the known design variables and objectives, which are given as inputs to the analysis tool. The analysis tool plots the coupling data versus layup angle. From this the best layup angles for a sought-after bend-twist couple is used to aeroelastically tailor the wing. The composite structure analysis tool’s accuracy was verified by analysing cantilever beam deflections and comparing the results with hand calculations and SolidWorks Simulation FEM results. The analysis tool’s accuracy was further verified by comparing the aerodynamic torsional load’s twist deflections with thin walled tube theory. The analysis tool was validated by applying a torsional load at the tip of a JS1C production Flaperon 3 in an experimental setup and then comparing this result with the Flaperon 3 modelled in the analysis tool. These comparisons also ensured that the model’s composite material properties and the meshing of the flaperon cross-sectional properties were correct. This aeroelastic tailoring was validated with the advantage of then being used to improve the aerodynamic performance of the JS1C Revelation 21 m tip’s flaperon. This improvement could be made by making use of a tailored bend-twist couple to reduce the effect of the aerodynamic load’s twist deflections. A test sample of the JS1C 21 m flaperon 3 was used to validate aeroelastic tailoring. The test sample was designed to be 1 m in length and have all the specified tailoring coupling characteristics that could improve the aerodynamic performance of the JS1C 21 m flaperon 3. The test sample was manufactured according to Jonker Sailplanes manufacturing standards and experimentally set up with the same applied deflections as in the analysis tool. The calculated bend-twist values and the experimental setup results were similar with a negligible difference, assuming small displacements and an aspect ratio greater than 13; this confirmed that the PreVABS/VABS/GEBT composite structure analysis tool could be used in aeroelastic tailoring to predict and design the bend-twist couple needed to improve the aerodynamic performance of the JS1C 21 m. While the twist behaviour of Flaperon 3 was improved by the tailored bend-twist couple, it was still necessary to add pre-twist as well, to fully address the effects of twisting by aerodynamic forces. / MIng (Mechanical Engineering), North-West University, Potchefstroom Campus, 2014

The aim of this investigation was to review literature for the most suitable aeroelastic tailoring analysis tools for long slender composite structures, and integrate them into an aeroelastic tailoring process. The JS1C Revelation is a high performance sailplane made from modern composites, mostly carbon fibre. This has the advantage of being more rigid than traditional engineering materials, thereby reducing the effects of the twisting deflections on these long slender structures due to aerodynamic loads. The implementing of aeroelastic tailoring can create bend-twist couples for performance improvements. Composites enable the use of aeroelastic tailoring to improve gliding performance. Flaperon 3 of the JS1C 21 m was used as the design problem for aeroelastic tailoring. Aeroelastic tailoring was done by analysing the flaperon structure at the different layup angles to determine the correct design point to tailor the structure to improve aerodynamic performance at thermalling and cruise, but mostly cruise since it accounts for 70% of the flight time. The composite structure analysis tool has the objective to get results during concept design. This directed the line of research of analysis tools to a solution method of two dimensional cross-section mesh properties projected onto a one dimensional beam. The literature of Hodges had good verification and published data on the analysis tools. The analysis tools comprised of three programs that were not very user friendly. Thus the author compiled a Matlab program as a user interface tool to run the three programs together. The aeroelastic tailoring process systematically works through the known design variables and objectives, which are given as inputs to the analysis tool. The analysis tool plots the coupling data versus layup angle. From this the best layup angles for a sought-after bend-twist couple is used to aeroelastically tailor the wing. The composite structure analysis tool’s accuracy was verified by analysing cantilever beam deflections and comparing the results with hand calculations and SolidWorks Simulation FEM results. The analysis tool’s accuracy was further verified by comparing the aerodynamic torsional load’s twist deflections with thin walled tube theory. The analysis tool was validated by applying a torsional load at the tip of a JS1C production Flaperon 3 in an experimental setup and then comparing this result with the Flaperon 3 modelled in the analysis tool. These comparisons also ensured that the model’s composite material properties and the meshing of the flaperon cross-sectional properties were correct. This aeroelastic tailoring was validated with the advantage of then being used to improve the aerodynamic performance of the JS1C Revelation 21 m tip’s flaperon. This improvement could be made by making use of a tailored bend-twist couple to reduce the effect of the aerodynamic load’s twist deflections. A test sample of the JS1C 21 m flaperon 3 was used to validate aeroelastic tailoring. The test sample was designed to be 1 m in length and have all the specified tailoring coupling characteristics that could improve the aerodynamic performance of the JS1C 21 m flaperon 3. The test sample was manufactured according to Jonker Sailplanes manufacturing standards and experimentally set up with the same applied deflections as in the analysis tool. The calculated bend-twist values and the experimental setup results were similar with a negligible difference, assuming small displacements and an aspect ratio greater than 13; this confirmed that the PreVABS/VABS/GEBT composite structure analysis tool could be used in aeroelastic tailoring to predict and design the bend-twist couple needed to improve the aerodynamic performance of the JS1C 21 m. While the twist behaviour of Flaperon 3 was improved by the tailored bend-twist couple, it was still necessary to add pre-twist as well, to fully address the effects of twisting by aerodynamic forces. / MIng (Mechanical Engineering), North-West University, Potchefstroom Campus, 2014

This work aims at dimensional reduction of nonlinear material models in an asymptotically accurate manner. The three-dimensional(3-D) nonlinear material models considered include isotropic, orthotropic and dielectric compressible hyperelastic material models. Hyperelastic materials have potential applications in space-based inflatable structures, pneumatic membranes, replacements for soft biological tissues, prosthetic devices, compliant robots, high-altitude airships and artificial blood pumps, to name a few. Such structures have special engineering properties like high strength-to-mass ratio, low deflated volume and low inflated density. The majority of these applications imply a thin shell form-factor, rendering the problem geometrically nonlinear as well. Despite their superior engineering properties and potential uses, there are no proper analysis tools available to analyze these structures accurately yet efficiently. The development of a unified analytical model for both material and geometric nonlinearities encounters mathematical difficulties in the theory but its results have considerable scope. Therefore, a novel tool is needed to dimensionally reduce these nonlinear material models. In this thesis, Prof. Berdichevsky’s Variational Asymptotic Method(VAM) has been applied rigorously to alleviate the difficulties faced in modeling thin shell structures(made of such nonlinear materials for the first time in the history of VAM) which inherently exhibit geometric small parameters(such as the ratio of thickness to shortest wavelength of the deformation along the shell reference surface) and physical small parameters(such as moderate strains in certain applications). Saint Venant-Kirchhoff and neo-Hookean 3-D strain energy functions are considered for isotropic hyperelastic material modeling. Further, these two material models are augmented with electromechanical coupling term through Maxwell stress tensor for dielectric hyperelastic material modeling. A polyconvex 3-D strain energy function is used for the orthotropic hyperelastic model. Upon the application of VAM, in each of the above cases, the original 3-D nonlinear electroelastic problem splits into a nonlinear one-dimensional (1-D) through-the-thickness analysis and a nonlinear two-dimensional(2-D) shell analysis. This greatly reduces the computational cost compared to a full 3-D analysis. Through-the-thickness analysis provides a 2-D nonlinear constitutive law for the shell equations and a set of recovery relations that expresses the 3-D field variables (displacements, strains and stresses) through thethicknessintermsof2-D shell variables calculated in the shell analysis (2-D). Analytical expressions (asymptotically accurate) are derived for stiffness, strains, stresses and 3-D warping field for all three material types. Consistent with the three types of 2-D nonlinear constitutive laws,2-D shell theories and corresponding finite element programs have been developed. Validation of present theory is carried out with a few standard test cases for isotropic hyperelastic material model. For two additional test cases, 3-Dfinite element analysis results for isotropic hyperelastic material model are provided as further proofs of the simultaneous accuracy and computational efficiency of the current asymptotically-correct dimensionally-reduced approach. Application of the dimensionally-reduced dielectric hyperelastic material model is demonstrated through the actuation of a clamped membrane subjected to an electric field. Finally, the through-the-thickness and shell analysis procedures are outlined for the orthotropic nonlinear material model.