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In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective. [ABSTRACT FROM AUTHOR]

The Rayleigh–Ritz method is widely employed to analyze free vibrations of elastic solids and structures. For a simple formulation and efficient evaluation of vibrations of elastic ellipsoids, which also include spheres, the Cartesian coordinate system is utilized. It is hoped that the formulation with lengthy expressions can be solved with fewer terms of displacement functions in Chebyshev polynomials for simple evaluations of stiffness and mass matrices of the elastic ellipsoids with the procedure. The vibrations of elastic ellipsoids are calculated with geometric parameters for the validation of the procedure and formulation with known results and the analysis from this study. [ABSTRACT FROM AUTHOR]

With large accelerations, the mechanical vibrations of device structures can be driven to nonlinear states yielding strong variations of vibration characteristics such as frequency change and modes shape distortions. The exact equation of motion with an external acceleration of the thickness-shear vibrations of an infinite isotropic plate is approximated through the coupling in frequencies and solved with harmonics matching, and the approximate solutions of frequency and displacements due to the acceleration are obtained. The analytical solution with good accuracy is obtained and the frequency variation is evaluated with the simple relationship between deformation, acceleration, and frequency. [ABSTRACT FROM AUTHOR]

With the advances of material processing technology and miniaturization of mechanical devices and components, it is clear now that curvilinear coordinate systems in dealing with special configurations of elastic solids including cylinders are also naturally needed in the analytical process. By adopting the cylindrical coordinates, it is found that the Love wave in semi-infinite solids possess the same velocity as in the Cartesian coordinates, but the displacement is dependent on radius near the origin and decaying slowly with the radius by exhibiting a strong contrast of the uniform displacement in the Cartesian formulation. Numerical examples show that the asymptotic approximation is accurate in one wavelength away from the origin, implying that solutions will be different only in the vicinity of the point of excitation. [ABSTRACT FROM AUTHOR]

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The frequency-temperature behavior has long been analyzed to ensure the smoothness of functioning frequency of a quartz crystal resonator during the temperature variation and maintain its operations in a stable state. It has been proven that vibrations of quartz crystal plates in the thickness-shear mode can be well described by the theory of incremental thermal field in conjunction with the Mindlin plate equations, demonstrating the possibility that vibration frequencies and mode shapes can also be well predicted with the temperature as a targeted variable. By studying the vibrations with temperature changes in a given range, the frequencies and vibration modes can be calculated as a function of temperature, then they can be used in the calculations of both strain and kinetic energies for vibration mode identification or characterization based on energy proportion and changes. The trends of changes of vibration frequency, amplitudes, and energy with temperature variation make it possible for characterization the variations of vibrations and particularly the weakening or enhancement of the dominance of specific vibration modes. With such relations between vibration properties and temperature known, possible analytical tools can be developed to aid the optimal design by avoiding significant mode changes or occurrences of mode conversion. [ABSTRACT FROM AUTHOR]

The scalar differential equation in the thickness eigendisplacement for the doubly-rotated quartz plates is applied to analyze thickness vibrations of an unelectroded circular plate with free edges at the neighborhood of the pure thickness vibration mode. The scalar differential equation is transformed into an elliptical coordinate system. With the boundary conditions of free edges, the frequencies and the modes are solved in terms of the Mathieu function and the Modified Mathieu function. The results of frequencies of the fundamental harmonic and its third overtone of an AT-cut quartz circular plate by the present approach agree well with the existing theoretical results and the experiment results. The frequencies and modes of an SC-cut quartz circular plate are investigated by the present approach. The frequencies are close to each other when the order of the harmonics is the same. A rotation angle of the symmetric axes of the vibration modes are observed that is dependent on the anisotropic material constants and the order of the harmonics. This approach has potential applications in the design of the doubly-rotated quartz circular resonators. [ABSTRACT FROM AUTHOR]

Due to the inherent viscosity of polymer, piezoelectric response in the thickness direction (d33) of cellular ferroelectret films usually depends on the time of measurement. In this letter, the micromechanical theory of viscoelastic composite was extended to predict the time dependence of the overall piezoelectric d33 coefficient of voided charged polymer foam. Experiments were carried out to find the time spectra of piezoelectric d33 coefficient of voided charged polypropylene film. Theoretical simulation agrees well with experiment data. [ABSTRACT FROM AUTHOR]

Quantifying the temporal and spatial patterns of impervious surfaces (IS) is important for assessing the environmental and ecological impacts of urbanization. In order to better extract IS, and to explore the divergence in urbanization in different regions, research on the regional differentiation features and regional change difference features of IS are required. To extract China's 2013 urban impervious area, we used the 2013 night light (NTL) data and the Moderate Resolution Imaging Spectroradiometer Normalized Difference Vegetation Index and enhanced vegetation index (EVI) temporal series data, and used three urban impervious surface extraction indexes—Human Settlements Index, Vegetation-Adjusted NTL Urban Index, and the EVI-adjusted NTL index (EANTLI)—which are recognized as the best and most widely used indexes for extracting urban impervious areas. We used the classification results of the Landsat-8 images as the benchmark data to visually compare and verify the results of the urban impervious area extracted by the three indexes. We determined that the EANTLI index better reflects the distribution of the impervious area. Therefore, we used the EANTLI index to extract the urban impervious area from 2003 to 2013 in the study area, and researched the spatial and temporal differentiation in urban IS. The results showed that China's urban IS area was 70,179.06 km2, accounting for 0.73% of the country's land area in 2013, compared with 20,565.24 km2 in 2003, which accounted for 0.21% of the land area, representing an increase of 0.52%. On a spatial scale, like economic development, the distribution of urban impervious surfaces was different in different regions. The overall performance of the urban IS percentage was characterized by a decreasing trend from Northwest China, Southwest China, the Middle Reaches of the Yellow River, Northeast China, the Middle Reaches of the Yangtze River, Southern Coastal China, and Northern Coastal China to Eastern Coastal China. On the provincial scale, the urban IS expansion showed considerable differences in different regions. The overall performance of the Urban IS Expansion index showed that the eastern coastal areas had higher values than the western inland areas. The cities or provinces of Beijing, Tianjin, Jiangsu, and Shanghai had the largest growth in impervious areas. Spatially and temporally quantifying the change in urban impervious areas can help to better understand the intensity of urbanization in a region. Therefore, quantifying the change in urban impervious area has an important role in the study of regional environmental and economic development, policy formulation, and the rational use of resources in both time and space. [ABSTRACT FROM AUTHOR]