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Compressible fluid flow problems were solved using an adaptive finite element method. Supersonic flow past a wedge and Prandtl-Meyer expansion were considered. Computational grids are presented.
Analytical formulations are developed to account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. The coupled response is captured at the material level through the thermopiezoelectric constitutive equations and leads to the inherent capability to model both the sensory and active responses of piezoelectric materials. A layerwise laminate theory is incorporated to provide more accurate analysis of the displacements, strains, stresses, electric fields, and thermal fields through-the-thickness. Thermal effects which arise from coefficient of thermal expansion mismatch, pyroelectric effects, and temperature dependent material properties are explicitly accounted for in the formulation. Corresponding finite element formulations are developed for piezoelectric beam, plate, and shell elements to provide a more generalized capability for the analysis of arbitrary piezoelectric composite structures. The accuracy of the current formulation is verified with comparisons from published experimental data and other analytical models. Additional numerical studies are also conducted to demonstrate additional capabilities of the formulation to represent the sensory and active behaviors. A future plan of experimental studies is provided to characterize the high temperature dynamic response of piezoelectric composite materials.
The objective of this calculation is to provide thermal profiles, heat dissipation and refractory thermal expansion results from changes to inputs/assumptions related to optimization of margins and conservatisms (described in Section 3).
Double-side cooled power modules are being developed for next-generation traction inverters due to their better heat extraction, lower profile, and lower parasitic inductances. However, due to their rigid structure, they cause reliability concerns arising from high thermo-mechanical stresses at the interconnection joints in the module. In this work, a materials-based approach using rigid encapsulants is presented for reducing thermo-mechanical fatigue. Finite-element thermo- mechanical simulations were performed to examine the effects of the elastic modulus and coefficient of thermal expansion of epoxy- based encapsulants on the bond deformation inside a double-side cooled power module. It was found that a rigid encapsulant with a high modulus of 6.0 GPa or above and a coefficient of thermal expansion around 20 ppm/oC would improve the thermo- mechanical reliability of double-side cooled power modules by decreasing the permanent bond deformation inside the modules by 50-60%.
Thermal barrier coatings (TBC) for advanced gas turbine blades have been under intensive development during the last several years. This investigation is intended to achieve a clearer understanding of the mechanical behavior of plasma sprayed zirconia-yttria TBCs, involving a nickle-chromium-aluminum bond coat. The near term objectives are to study the stress states in a relatively simple model TBC subjected to steady state thermal loading. The resulting thermal expansion mismatch and oxidation have been primary targets for the study. The finite element approach and the effects of thermal mismatch and oxidation are described. A proposed mechanism for oxidation induced coating failure is also presented.
A new piezoceramic strut has been developed. This strut utilizes strain induced bending as a means of actuation. The significance of this design is that the displacement of the strut's motion arm is independent of the expansion of the piezoceramic material. Design criteria was developed using continuous and finite element modeling techniques. Experimental and analytical results were compared. Finally, a numerical analysis was conducted that demonstrated the benefits of the piezoceramic strut configuration.
The objective is to develop micromechanical models for predicting the stiffness and strength properties of textile composite materials. Two models are presented to predict the homogeneous elastic constants and coefficients of thermal expansion of a textile composite. The first model is based on rigorous finite element analysis of the textile composite unit-cell. Periodic boundary conditions are enforced between opposite faces of the unit-cell to simulate deformations accurately. The second model implements the selective averaging method (SAM), which is based on a judicious combination of stiffness and compliance averaging. For thin textile composites, both models can predict the plate stiffness coefficients and plate thermal coefficients. The finite element procedure is extended to compute the thermal residual microstresses, and to estimate the initial failure envelope for textile composites.
The 3D Ising conformal field theory (CFT) describes different physical systems, such as uniaxial magnets or fluids, at their critical points. In absence of an analytical solution for the 3D Ising model, the scaling dimensions and operator product expansion (OPE) coefficients characterizing this CFT must be determined numerically. The currently most-cited values for these quantities have been obtained from the conformal bootstrap, while lattice calculations have so far only produced reliable results for the scaling dimensions involved in calculating the critical exponents. Using Quantum Finite Elements to investigate critical \(\phi^4\)-theory on \(\mathbb{R}\times\mathbb{S}^2\), we show in this work that it is possible to extract scaling dimensions and OPE coefficients of the 3D Ising CFT by fitting the lattice four-point function with expectations from the operator product expansion for the radially quantized CFT and extrapolating to the continuum limit. This way, we have for the first time been able to use Monte Carlo simulations to compute the central charge of the theory.
In an effort to understand how the lung is deformed by its own weight, we have analyzed the distribution of regional expansion, stresses, and surface pressures in a theoretical elastic lung-shaped model using the technique of finite elements. In the upright position, the parenchyma was most expanded at the apex and least at the base. Stresses in both the vertical and lateral directions were maximal at the apex. As the lung was inflated from very low volumes to total lung capacity, parenchymal expansion and stress at the apex first decreased, then increased. This behavior can be explained by the increasing rigidity of the expanded lung which enabled it to resist distortion by its own weight. At functional residual capacity, the stress at the apex was near its minimum. The differences in intrapleural pressure down the lung were volume dependent, increasing at very low volumes. In the inverted lung, the regional differences in stress, strain, and surface pressures were less marked because of the shape of the chest.
This paper reports the development of a 3D mesoscale hygro-thermal-mechanical simulation approach to predict damage in concrete irradiated in a test reactor. This framework, developed in MOOSE, considers the effects of elevated temperature, moisture content, and high neutron fluence (energy threshold, E > 0.1 MeV) on the mortar and aggregates separately. The first-stage simulation implements hygro-thermal analysis to determine the temperature and RH inside the specimen as a function of imposed radiation energy. These are used as inputs to the second stage, which considers radiation-induced volumetric expansion (RIVE) of aggregates, and creep, shrinkage, and stress-strain response of mortar to predict the expansion, stresses, and damage in specimens made using different coarse aggregates and subjected to different irradiation times. The irradiation time-dependent damage in the mortar is expressed using an isotropic damage parameter. This multi-physics model serves as a predictive tool for damage quantification in concrete due to neutron irradiation.
A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step, computed deflection along the fibers are combined with a finite element model of the structure in order to interpolate and extrapolate the deflection and slope of the entire structure through the use of the System Equivalent Reduction and Expansion Process. The theory is first validated on a computational model, a cantilevered rectangular plate wing. The theory is then applied to test data from a cantilevered swept-plate wing model. Computed results are compared with finite element results, results using another strainbased method, and photogrammetry data. For the computational model under an aeroelastic load, maximum deflection errors in the fore and aft, lateral, and vertical directions are -3.2%, 0.28%, and 0.09%, respectively; and maximum slope errors in roll and pitch directions are 0.28% and -3.2%, respectively. For the experimental model, deflection results at the tip are shown to be accurate to within 3.8% of the photogrammetry data and are accurate to within 2.2% in most cases. In general, excellent matching between target and computed values are accomplished in this study. Future refinement of this theory will allow it to monitor the deflection and health of an entire aircraft in real time, allowing for aerodynamic load computation, active flexible motion control, and active induced drag reduction.
A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step, computed deflection along the fibers are combined with a finite element model of the structure in order to interpolate and extrapolate the deflection and slope of the entire structure through the use of the System Equivalent Reduction and Expansion Process. The theory is first validated on a computational model, a cantilevered rectangular plate wing. The theory is then applied to test data from a cantilevered swept-plate wing model. Computed results are compared with finite element results, results using another strain-based method, and photogrammetry data. For the computational model under an aeroelastic load, maximum deflection errors in the fore and aft, lateral, and vertical directions are -3.2 percent, 0.28 percent, and 0.09 percent, respectively; and maximum slope errors in roll and pitch directions are 0.28 percent and -3.2 percent, respectively. For the experimental model, deflection results at the tip are shown to be accurate to within 3.8 percent of the photogrammetry data and are accurate to within 2.2 percent in most cases. In general, excellent matching between target and computed values are accomplished in this study. Future refinement of this theory will allow it to monitor the deflection and health of an entire aircraft in real time, allowing for aerodynamic load computation, active flexible motion control, and active induced drag reduction..
Numerical tools, such as the finite-element method, are increasingly used to design and evaluate the photovoltaic (PV) modules, providing for the reduction of development time and improved performance and reliability. However, high-fidelity material models are necessary to accurately model the complex structural behavior of the involved packaging materials. A common simplification used in recent years is to model the polymer materials (i.e., encapsulant and backsheet) as linear elastic, which will lead to inaccurate results. Therefore, in this work, we present a thorough characterization of the time- and temperature-dependent mechanical response of predominant PV module encapsulant and backsheet materials. Based on this material characterization, we developed and experimentally validated generalized Maxwell models to describe each material's viscoelastic response. In addition, we included measurements of the coefficient of thermal expansion and presented all material models in such a fashion for direct input into commercial finite-element method modeling software.
Accurate, passive, and wireless monitoring of cryogenic hardware is essential for high-energy physics, space propulsion, and biomedical instrumentation. Here, this study quantifies the coupled temperature-strain behavior of Rayleigh-mode surface acoustic-wave (SAW) delay-line sensors fabricated on 128° YX-cut LiNbO 3 . A nonlinear finite element (FE) model incorporating Varshni-based elastic constants, higher-order thermal expansion, and temperature-dependent piezo- and dielectric coefficients was developed and validated experimentally between 280K and 80K. Free-standing (first test condition) and bonded/wired (second test condition) devices exhibited indistinguishable thermal responses; the average temperature coefficient of delay (TCD) in the critical cryogenic range from 130K down to 80K differed by only 0.15 ppm/K (0.32%), confirming that bonding-induced stress is negligible. Over 280-80K the measured TCD was 61.77 ppm/K, while the FE model predicted an equivalent temperature coefficient of frequency (TCF) of −62.74 ppm/K with an overall coefficient of determination R2 = 0.998. In the critical cryogenic interval 130-80K the TCD fell to 47.66 ppm/K, indicating improved thermal stability at low temperature. Controlled loading (0-300 με) revealed a strain coefficient of delay (SCD) that rises from 0.53 ± 0.02 ppm/με at 300K to 1.05 ± 0.02 ppm/με at 80K. This modest sensitivity confirms that, for temperature sensing, strain is a second-order perturbation above 135K but must be compensated at deeper cryogenic levels. Overall, this work establishes a predictive multiphysics model together with repeatable wired measurements that confirm the suitability of SAW sensors for temperature and strain monitoring in extreme cryogenic environments, while also providing a baseline for future wireless implementations.
To understand better the effect of shape and size of lung and chest wall on the distribution of stresses, strains, and surface pressures, we analyzed a theoretical model using the technique of finite elements. First we investigated the effects of changing the chest wall shape during expansion, and second we studied lungs of a variety of inherent shapes and sizes. We found that, in general, the distributions of alveolar size, mechanical stresses, and surface pressures in the lungs were dominated by the weight of the lung and that changing the shape of the lung or chest wall had relatively little effect. Only at high states of expansion where the lung was very stiff did changing the shape of the chest wall cause substantial changes. Altering the inherent shape of the lung generally had little effect but the topographical differences in stresses and surface pressures were approximately proportional to lung height. The results are generally consistent with those found in the dog by Hoppin et al (1969).
Space simulated thermally induced deformations and stresses in continuous fiber reinforced composites were investigated with a micromechanics analysis. The investigation focused on two primary areas. First, available explicit expressions for predicting the effective coefficients of thermal expansion (CTEs) for a composite were compared with each other, and with a finite element (FE) analysis, developed specifically for this study. Analytical comparisons were made for a wide range of fiber/matrix systems, and predicted values were compared with experimental data. The second area of investigation focused on the determination of thermally induced stress fields in the individual constituents. Stresses predicted from the FE analysis were compared to those predicted from a closed-form solution to the composite cylinder (CC) model, for two carbon fiber/epoxy composites. A global-local formulation, combining laminated plate theory and FE analysis, was used to determine the stresses in multidirectional laminates. Thermally induced damage initiation predictions were also made.
The experimental study of a piezoceramic active truss is presented. This active strut is unique in that the piezoceramic configurations allow the stroke length of the strut not to be dependent on the piezoceramic material's expansion range but on the deflection range of the piezoceramic bender segment. A finite element model of a piezoceramic strut segment was constructed. Piezoceramic actuation was simulated using thermally induced strains. This model yielded information on the stiffness and force range of a bender element. The static and dynamic properties of the strut were identified experimentally. Feedback control was used to vary the stiffness of the strut. The experimentally verified model was used to explore implementation possibilities of the strut.
The stress derivative technique for control of keystoning deformation in under-integrated finte elements is based on expansion of the stress in a Taylor series about the element center and retention of additional terms beyond the constant stress term. It has the advantage over other control techniques that keystoning resistance is provided by actual rather than artificial material properties. Application of this technique to the quadrilateral ring elements used for modelling solids of revolution subjected to axisymmetric loads is described. In a cylindrical coordinate system additional terms appear in the formulation which must be dealt with in arriving at a workable keystoning control scheme.