Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

Application of finite element method and photo-elasticity to an lap welded connection

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Mechanical properties and the evolution of matrix molecules in PTFE upon irradiation with MeV alpha particles

The morphology, chemical composition, and mechanical properties in the surface region of α-irradiated polytetrafluoroethylene (PTFE) have been examined and compared to unirradiated specimens. Samples were irradiated with 5.5 MeV 4He2+ ions from a tandem accelerator to doses between 1 × 106 and 5 × 1010 Rad. Static time-of-flight secondary ion mass spectrometry (ToF-SIMS), using a 20 keV C60+ source, was employed to probe chemical changes as a function of a dose. Chemical images and high resolution spectra were collected and analyzed to reveal the effects of a particle radiation on the chemical structure. Residual gas analysis (RGA) was utilized to monitor the evolution of volatile species during vacuum irradiation of the samples. Scanning electron microscopy (SEM) was used to observe the morphological variation of samples with increasing a particle dose, and nanoindentation was engaged to determine the hardness and elastic modulus as a function of a dose. The data show that PTFE nominally retains its innate chemical structure and morphology at a doses <109 Rad. At α doses ≥109 Rad the polymer matrix experiences increased chemical degradation and morphological roughening which are accompanied by increased hardness and declining elasticity. At  α doses >1010 Rad the polymer matrix suffers severe chemical degradation and material loss. Chemical degradation is observed in ToF-SIMS by detection of ions that are indicative of fragmentation, unsaturation, and functionalization of molecules in the PTFE matrix. The mass spectra also expose the subtle trends of crosslinking within the α-irradiated polymer matrix. ToF-SIMS images support the assertion that chemical degradation is the result of a particle irradiation and show morphological roughening of the sample with increased a dose. High resolution SEM images more clearly illustrate the morphological roughening and the mass loss that accompanies high doses of a particles. RGA confirms the supposition that the outcome of chemical degradation in the PTFE matrix with continuing irradiation is evolution of volatile species resulting in morphological roughening and mass loss. Finally, we reveal and discuss relationships between chemical structure and mechanical properties such as hardness and elastic modulus.

Characterizing permanent deformation and fracture of asphalt mixtures by using compressive dynamic modulus tests

Permanent deformation and fracture may develop simultaneously when an asphalt mixture is subjected to a compressive load. The objective of this research is to separate viscoplasticity and viscofracture from viscoelasticity so that the permanent deformation and fracture of the asphalt mixtures can be individually and accurately characterized without the influence of viscoelasticity. The undamaged properties of 16 asphalt mixtures that have two binder types, two air void contents, and two aging conditions are first obtained by conducting nondestructive creep tests and nondestructive dynamic modulus tests. Testing results are analyzed by using the linear viscoelastic theory in which the creep compliance and the relaxation modulus are modeled by the Prony model. The dynamic modulus and phase angle of the undamaged asphalt mixtures remained constant with the load cycles. The undamaged asphalt mixtures are then used to perform the destructive dynamic modulus tests in which the dynamic modulus and phase angle of the damaged asphalt mixtures vary with load cycles. This indicates plastic evolution and crack propagation. The growth of cracks is signaled principally by the increase of the phase angle, which occurs only in the tertiary stage. The measured total strain is successfully decomposed into elastic strain, viscoelastic strain, plastic strain, viscoplastic strain, and viscofracture strain by employing the pseudostrain concept and the extended elastic-viscoelastic correspondence principle. The separated viscoplastic strain uses a predictive model to characterize the permanent deformation. The separated viscofracture strain uses a fracture strain model to characterize the fracture of the asphalt mixtures in which the flow number is determined and a crack speed index is proposed. Comparisons of the 16 samples show that aged asphalt mixtures with a low air void content have a better performance, resisting permanent deformation and fracture. © 2012 American Society of Civil Engineers.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Comparative physical, mechanical and crystallographic properties of a series of gemfibrozil salts

Objectives Understanding the impact of the counterion on the properties of an acidic or basic drug may influence the choice of salt form, especially for less potent drugs with a high drug load per unit dose. The aim of this work was to determine the influence of the hydrogen bonding potential of the counterion on the crystal structure of salts of the poorly soluble, poorly compressible, acidic drug gemfibrozil and to correlate these with mechanical properties. Methods Compacts of the parent drug and the salts were used to determine Young's modulus of elasticity using beam bending tests. Crystal structures were determined previously from X-ray powder diffraction data. Key findings The free acid, tert-butylamine, 2-amino-2-methylpropan-1-ol and 2-amino-2-methylpropan-1, 3-diol salts had a common crystal packing motif of infinite hydrogen-bonded chains with cross-linking between pairs of adjacent chains. The tromethamine (trsi) salt, with different mechanical properties, had a two-dimensional sheet-like network of hydrogen bonds, with slip planes, forming a stiffer compact. Conclusions The type of counter ion is important in determining mechanical properties and could be selected to afford slip and plastic deformation. © 2010 Royal Pharmaceutical Society of Great Britain.

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) microelectromechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2 Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature. ^

Novel hybrid columns made of ultra-high performance concrete and fiber reinforced polymers

The application of advanced materials in infrastructure has grown rapidly in recent years mainly because of their potential to ease the construction, extend the service life, and improve the performance of structures. Ultra-high performance concrete (UHPC) is one such material considered as a novel alternative to conventional concrete. The material microstructure in UHPC is optimized to significantly improve its material properties including compressive and tensile strength, modulus of elasticity, durability, and damage tolerance. Fiber-reinforced polymer (FRP) composite is another novel construction material with excellent properties such as high strength-to-weight and stiffness-to-weight ratios and good corrosion resistance. Considering the exceptional properties of UHPC and FRP, many advantages can result from the combined application of these two advanced materials, which is the subject of this research. The confinement behavior of UHPC was studied for the first time in this research. The stress-strain behavior of a series of UHPC-filled fiber-reinforced polymer (FRP) tubes with different fiber types and thicknesses were tested under uniaxial compression. The FRP confinement was shown to significantly enhance both the ultimate strength and strain of UHPC. It was also shown that existing confinement models are incapable of predicting the behavior of FRP-confined UHPC. Therefore, new stress-strain models for FRP-confined UHPC were developed through an analytical study. In the other part of this research, a novel steel-free UHPC-filled FRP tube (UHPCFFT) column system was developed and its cyclic behavior was studied. The proposed steel-free UHPCFFT column showed much higher strength and stiffness, with a reasonable ductility, as compared to its conventional reinforced concrete (RC) counterpart. Using the results of the first phase of column tests, a second series of UHPCFFT columns were made and studied under pseudo-static loading to study the effect of column parameters on the cyclic behavior of UHPCFFT columns. Strong correlations were noted between the initial stiffness and the stiffness index, and between the moment capacity and the reinforcement index. Finally, a thorough analytical study was carried out to investigate the seismic response of the proposed steel-free UHPCFFT columns, which showed their superior earthquake resistance, as compared to their RC counterparts.

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) MicroElectroMechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature.

Tratamento de argila montmorilonítica para a produção de nanocompósitos poliméricos com retardo de propagação de chama

Compared to conventional composites, polymer matrix nanocomposites typically exhibit enhanced properties at a significantly lower filler volume fraction. Studies published in the literature indicate t hat the addition of nanosilicate s can increase the resistance to flame propagation in polymers. In this work, a treatment of montmorillonite (MMT) nano clay and the effect of its ad dition o n flame propagation characteristics of vinyl ester were studied. The resea rch was conducted in two stages. The first stage focused on the purification and activation of the MMT clay collected from a natural deposit to improve compatibility with the polymer matrix . Clay modification with sodium acetate was also studied to improve particle dispersion in the polymer. The second step was focused on the effect of the addition of the treated clay on nanocomposites ’ properties. Nanocomposites with clay con tents of 1, 2, 4 wt. % were processed. T he techniques for the characterization of the clay included X - ray fluorescence (XRF), X - r ay d iffraction (XRD), thermogravimetric a nalysis (TGA), d ifferential scanning c alorimetry (DSC) , s urface area (BET) and Fourier transform infrared spectroscopy (FTIR). For t he characterization of the nanocomposites , the techniques used were thermogravimetric a nalysis (TGA) , differential scanning c alorimetry (DSC), Fourier transform infrared spectroscopy (FTIR) , scanning electron mi croscopy (SEM), transmission electron m icroscopy (TEM), and the determination of tensile strength, modulus of elasticity and resistance to flame propagation. According to the results, the purification and activation treatment with freeze - drying used in thi s work for the montmorillonite clay was efficient to promote compatibility and dispersion in the polymer matrix as evidenced by the characterization of the nanocomposite s . It was also observed that the clay modifica tion using sodium acetate did not produce any significant effect to improve compatibilization of the clay with the polymer. The addition of the treated MMT resulted in a reduction of up to 53% in the polymer flame propagation speed and did not affect the mechanical tensile strength and modulus o f elas ticity of the polymer, indicating compatibility between the clay and polymer. The effectiveness in reducing flame propagation speed peaked for nanocomposites with 2 wt. % clay, indicating that this is the optimum clay concentration for this property. T he clay treatment used in this work enables the production of vinylester matrix nanocomposites with flame - retardancy properties .

Fabricação e caracterização de um compósito hibrido com resíduo lignocelulósico

This work aims to manufacture and characterize a hybrid plastic composite with the matrix isophthalic polyester resin base and having as reinforcing glass fiber and the dry endocarp of coconut (Coco nucifera Linn) in the form of particles as filler. The composite was made industrially in Tecniplas Industry and Trade LTDA. in the form of plate, and was manufactured process made by the manual lamination (Hand Lay Up). From the plate they were prepared test specimens for testing density, water absorption, uniaxial traction in dry and wet states, and testing of bending, as well as studies on the behavior of the generated fractures, macroscopic and microscopic, in mechanical tests through. All tests were performed in order to find the most viable applications the hybrid composite manufactured. The tensile and bending tests were analyzed last tensile properties, elasticity and deformation module. After the studies, it is observed that the percentage moisture absorbed was 3.03%. The presence of moisture in the tensile test meant a decrease of 19.77% from last stand, and 5.26% in the elastic modulus. For bending tests gave an average value of 69.13 MPa flexural strength. The results show the application of hybrid composite studied in lightweight structures, indoors, which require low / medium performance traction demands, and which involve flexural requests.

Measurements of stress-optic coefficient and Young's modulus in PMMA fibers drawn under different conditions

We have systematically measured the differential stress-optic coefficient, ΔC, and Young's modulus, E, in a number of PMMA fibers drawn with different stress, ranging from 2 up to 27 MPa. Effect of temperature annealing on those parameters was also investigated. ΔC was determined in transverse illumination by measuring the dependence of birefringence on additional axial stress applied to the fiber. Our results show that ΔC in PMMA fibers has a negative sign and ranges from -4.5 to -1.5×10-12 Pa -1 depending on the drawing stress. Increase of the drawing stress results in greater initial fiber birefringence and lower ΔC. The dependence of ΔC and initial birefringence upon drawing stress is nonlinear and gradually saturates for higher drawing stress. Moreover, we find that ΔC is linearly proportional to initial fiber birefringence and that annealing the fiber has no impact on the slope of this dependence. On the other hand, no clear dependence was observed between the fiber drawing stress and the Young's modulus of the fibers as measured using microscopic digital image correlation with the fibers tensioned using an Instron tension tester. © 2010 SPIE.

Radiological and material characterization of high volume fly ash concrete

The main goal of research presented in this paper was the material and radiological characterization of high volume fly ash concrete (HVFAC) in terms of determination of natural radionuclide content and radon emanation and exhalation coefficients. All concrete samples were made with a fly ash content between 50% and 70% of the total amount of cementitious materials from one coal burning power plant in Serbia. Physical (fresh and hardened concrete density) and mechanical properties (compressive strength, splitting tensile strength and modulus of elasticity) of concrete were tested. The radionuclide content (226Ra, 232Th and 40K) and radon massic exhalation of HVFAC samples were determined using gamma spectrometry. Determination of massic exhalation rates of HVFAC and its components using radon accumulation chamber techniques combined with a radon monitor was performed. The results show a beneficial effect of pozzolanic activity since the increase in fly ash content resulted in an increase in compressive strength of HVFAC by approximately 20% for the same mass of cement used in the mixtures. On the basis of the obtained radionuclide content of concrete components the I -indices of different HVFAC samples were calculated and compared with measured values (0.27e0.32), which were significantly below the recommended 1.0 index value. The prediction was relatively close to the measured values as the ratio between the calculated and measured I-index ranged between 0.89 and 1.14. Collected results of mechanical and radiological properties and performed calculations clearly prove that all 10 designed concretes with a certain type of fly ash are suitable for structural and non-structural applications both from a material and radiological point of view.