cij: A Python code for quasiharmonic thermoelasticity
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Abstract Subduction of carbonate‐bearing oceanic plates into Earth's interior recycles carbon from the surface to the deep mantle. The subducted carbonates can significantly affect mantle properties and dynamics. Magnesite is recognized as one of the major potential carbon hosts in the deep mantle because of its stability up to deep lower mantle conditions. However, despite many previous studies on the equation of state and elastic properties of magnesite, large discrepancies still exist for its elastic moduli and their pressure and temperature derivatives. Here we report in situ density and elastic wave velocity measurements on a natural magnesite at simultaneous high pressure‐temperature conditions up to ∼8 GPa–1073 K in a multi‐anvil apparatus using ultrasonic and synchrotron X‐ray techniques. Global fitting of the data set to finite strain equations yieldsK S0 = 114.0 ± 1.2 GPa, = 4.9 ± 0.3, = (−0.019 ± 0.002) GPa/K,G 0 = 68.6 ± 0.4 GPa,G′ = 1.6 ± 0.1, and = (−0.018 ± 0.001) GPa/K. Compared to other major upper mantle and transition zone minerals, magnesite has intermediateV P , the lowestV S , and the lowest density. Thus, magnesite possesses higherV P /V S ratio than other mantle minerals in normal mantle regions, whereas this feature is less pronounced in subduction zone environments. Modeling of the velocity profiles of carbonated lithologies along different geotherms suggests that moderately‐enriched magnesite domains are unlikely to be detected seismically in the Earth's mantle.
The Martian mantle is considered to have a higher Fe/Mg ratio than the Earth's mantle. Ringwoodite, γ-(Mg,Fe) 2 SiO 4 , is likely the dominant polymorph of olivine in the core-mantle boundary (CMB) region of Mars. We synthesized anhydrous iron-rich ringwoodite with molar Mg/(Mg + Fe) = 0.44 and determined its thermal equation of state up to 35 GPa and 750 K by synchrotron X-ray diffraction. Using a third order Birch-Murnaghan equation of state, we obtain K T0 = 182 (3) GPa, K' = 4.6 (2), and α 0 = 3.18 (6) × 10 -5 K -1 . Using these results and an updated mineralogical model with an iron-rich composition of Mg/(Mg + Fe) = 0.75 for the Martian mantle, we estimate ~1900 K for the temperature of the D1000 seismic discontinuity inside Mars. The resulting adiabat predicts a warm aerotherm, which could explain the presence of partial melt at the CMB of Mars recently detected with seismic data from the 2019 InSight mission.
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Thermal flutter analysis of booms with open cross section
Anomalous spacecraft OGO-D motion explained by open section boom thermally induced oscillations, discussing corrective measures
Solar heating of cylindrical boom and thermal effects on OGO-D torsional characteristics
Announced report discusses experimental test program in which five different solar cell array designs were evaluated by subjecting them to 60 thermal cycles from minus 190 deg to 0.0 deg. Results indicate that solder-coated cells combined with Kovar n-interconnectors and p-interconnectors are more durable under thermal loading than other configurations.
Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiations. The partial differential equations for all the elements of the satellite are linear in the space dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations. In the succeeding paper, a further reduction of these equations is made into singular perturbation equations, which are amenable to solution for complex problems of extremely large number of degrees of freedom.
Accurate prediction of failure of solar cell arrays requires accuracy in the computation of thermally induced stresses. This was accomplished by using the finite element technique. Improved procedures for stress calculation were introduced together with failure criteria capable of describing a wide range of ductile and brittle material behavior. The stress distribution and associated failure mechanisms in the N-interconnect junction of two solar cell designs were then studied. In such stress and failure analysis, it is essential to know the thermomechanical properties of the materials involved. Measurements were made of properties of materials suitable for the design of lightweight arrays: microsheet-0211 glass material for the solar cell filter, and Kapton-H, Kapton F, Teflon, Tedlar, and Mica Ply PG-402 for lightweight substrates. The temperature-dependence of the thermal coefficient of expansion for these materials was determined together with other properties such as the elastic moduli, Poisson's ratio, and the stress-strain behavior up to failure.
Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells, have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiation. The partial differential equations for all the elements of the satellite are linear in the space-dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations.
An equation in the form of a Fourier series was derived in an earlier study to give displacements of the originally straight edge of a plate as the result of a small heat input patch moving at speed c along that edge. That unwieldly formulation is reduced to a simple integral equation, which is shown to be manageable in an example calculation. The integral equation is shown to be closely related to that of Ling and Mow, although it is much simpler to use. Comparison of the results of the simplification to results of the original series formulation suggest that the equation proposed for 'high Peclet number' may be a valid approximation for Peclet number as low as 2.5.
Many sealing configurations incorporate the geometry of line contact on bluff, slablike bodies. When sliding speed is sufficiently high along or across the line of contact, instabilities may arise from interactions of thermal expansion, elastic deformation and frictional heating. These lead to concentrated contact with elevated temperatures and pressures. Previous studies have been largely restricted to two-dimensional models of such contact. The present study shows how those earlier results must be modified to apply to the more realistic geometry, and show also that the principal features of the interactions are the same in both geometries.
Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.