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Among the main challenges in shape optimization is the coupling of Finite Element Method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multi-physics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. There are two mathematically equivalent approaches to computing the shape derivative: the volume method, and the boundary method. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. Prior implementations of shape derivatives at Sandia have been based on the volume method. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. The development of the strip method also offers us the opportunity to share some lessons learned about implementing the volume method and boundary method, to show shape optimization results on problems of interest, and to begin addressing the other main challenges at hand: constraints on optimized shapes, and their interplay with optimization algorithms.
Theoretical analyses for computer program to calculate random vibrations of reinforced rectangular cylindrical panels in fluctuating pressure environment
Users manual for computer program to calculate random vibrations of reinforced rectangular cylindrical panels in fluctuating pressure environments
Internal loads and stresses caused by space vehicle vibration resulting from induced or natural environments
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The infrared spectral intensities for HOCl and HO2 have been calculated using a new ab initio technique. Theoretical results for the geometries, vibrational frequencies, and the dipole moments of these species are also reported. All of the calculations were performed at the SCF level using near Hartree-Fock quality basis sets. The results for the molecular geometries and the vibrational frequencies are in good agreement with available experimental data. It is believed that the computed intensities are accurate to at least 50%. The results should be helpful in attempts to determine the stratospheric abundance of HOCl and HO2 by in situ infrared spectroscopic measurements.
Analytic derivative techniques are utilized to determine molecular geometries, vibration spectra, molecular force field, proton affinity, and energetics of clustering of protonated methane. It is observed that the geometries are gradient optimized, while the harmonic force fields and IR intensities are also determined analytically at the SCF level. It is determined that the frequency of the torsional model for rotation of the H2 about the pseudothreefold axis of the CH3(+) group is extremely low, and the proton affinity of CH4 is calculated as 129.0 kcal/mol.
The Lanczos (1950), multisectioning, and subspace iteration sequential methods for vibration analysis presently used as bases for three parallel algorithms are noted, in the aftermath of three example problems, to maintain reasonable accuracy in the computation of vibration frequencies. Significant computation time reductions are obtained as the number of processors increases. An analysis is made of the performance of each method, in order to characterize relative strengths and weaknesses as well as to identify those parameters that most strongly affect computation efficiency.
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Recent advances in the development of refined theories and their finite-element analyses of plates and shells are reviewed and sample results are presented. Both single-layer and layer-wise plate theories for the analysis of laminated composite plates and shells are discussed. The effect of element locking, physical symmetries and boundary conditions on natural frequencies are discussed, and the accuracy of various theories is evaluated. The layer-wise laminate theories developed by the author and his colleagues yield significantly more accurate results for laminated plates and shells with dissimilar layers than the conventional single-layer theories.
An experiment was performed on a rigid wall rectangular acoustic cavity driven by a flexible plate mounted in a quarter of one end wall and excited by white noise. The experiment was designed so that the assumptions of Asymptotic Modal Analysis (AMA) were satisfied for certain bandwidths and center frequencies. Measurements of sound pressure levels at points along the boundaries and incrementally into tbe interior were taken. These were compared with the theoretical results predicted with AMA, and found to be in good agreement, particularly for moderate (1/3 octave) bandwidths and sufficiently high center frequencies. Sound pressure level measurements were also taken well into the cavity interior at various points along the 5 totally rigid walls. The AMA theory, including boundary intensification effects, was shown to be accurate provided the assumption of large number of acoustic modes is satisfied, and variables such as power spectra of the wall acceleration, frequency, and damping are slowly varying in the frequency of bandwidth.
Quantum mechanical computational methods are employed for an ab initio investigation of: (1) the molecular properties of the lowest isomers of the ClO dimer; and (2) predicted molecular and thermochemical properties. Techniques employed include electron correlation and particularly singles and doubles coupled-cluster (CCSD) theory with or without perturbational estimates of the effects of connected triple excitations. The isomers ClOClO and ClClO2 are found to have higher energies than the ClOOCl isomer, and the theoretical vibrational frequencies of the isomers are well correlated with experimental data. Experimental values of the heat of formation for the isomers are also compared with calculations based on an isodesmic reaction with Cl2O, H2O, and HOOH.
A new method for commanding machines to move with increased dynamic performance was developed. This method is an enhanced version of input shaping, a patented vibration suppression algorithm. This technique intercepts a command input to a system command that moves the mechanical system with increased performance and reduced residual vibration. This document describes many advanced methods for generating highly optimized shaping sequences which are tuned to particular systems. The shaping sequence is important because it determines the trade off between move/settle time of the system and the insensitivity of the input shaping algorithm to variations or uncertainties in the machine which can be controlled. For example, a system with a 5 Hz resonance that takes 1 second to settle can be improved to settle instantaneously using a 0.2 shaping sequence (thus improving settle time by a factor of 5). This system could vary by plus or minus 15% in its natural frequency and still have no apparent vibration. However, the same system shaped with a 0.3 second shaping sequence could tolerate plus or minus 40% or more variation in natural frequency. This document describes how to generate sequences that maximize performance, sequences that maximize insensitivity, and sequences that trade off between the two. Several software tools are documented and included.
The XCN and XNC (X=F, Cl) isomers have been investigated using the CCSD and CCSD(T) methods in conjunction with a TZ2P basis set. Equilibrium geometries, dipole moments, harmonic frequencies, IR intensities and relative energies have been evaluated. The CCSD(T) geometries and vibrational frequencies for the XCN isomers are in good agreement with the available experimental data. The CCSD(T) results for FCN and FNC are in good agreement with the CEPA calculations of Botshwina et al., with the exception of the energy difference, which the CEPA method underestimates by about 1.2 kcal/mol. FCN and CICN are shown to be lower in energy than the FNC and ClNC isomers by 69.511.0 and 42.711.0 kcal/mol (0 K), respectively.