Three-dimensional Green’s function and its derivatives for anisotropic elastic, piezoelectric and magnetoelectroelastic materials

Diese Arbeit behandelt hauptsächlich die Greensche Funktion für lineare allgemein anisotrope Materialien im unendlichen dreidimensionalen Raum, die auch als Fundamentallösung bezeichnet wird. Die detaillierten Herleitungen und die numerischen Auswertungen der expliziten Ausdrücke der Greenschen Funktion bzw. deren ersten und zweiten Ableitung, die auf der Methode der Residuen (RCM), dem Stroh-Formalismus (SFM) sowie der Unified Explicit Expression Method (UEEM) basieren, werden ebenfalls behandelt. Die numerischen Beispiele der drei verschiedenen Methoden werden für die Elastizitätstheorie miteinander verglichen. In nicht-degenerierten Fällen sind alle drei Methoden exakt für einen beliebigen Punkt. Bei nahezu degenerierten Fällen werden sowohl die RCM als auch die SFM instabil, während die UEEM ihre Gültigkeit behält. Ungeachtet dessen ist die SFM etwas stabiler als die RCM. Um deren Instabilität in degenerierten und nahezu degenerierten Fällen zu überwinden, werden in der RCM und der SFM einige Materialkonstanten leicht modifiziert. Trotz der Vorteile der UEEM im Vergleich zu RCM und SFM, ergeben sich Schwierigkeiten bei der Erweiterung auf Mehrfeldmaterialien. Die RCM und die SFM werden auf piezoelektrische Materialien erweitert und miteinander verglichen. Dadurch, dass die SFM bessere Ergebnisse für piezoelektrische Materialien liefert als die RCM, wird sie zusätzlich auf magnetoelektroelastische Materialien erweitert. Darüber hinaus wird die UEEM als Anwendung in einem BEM-Programm implementiert, mit dem sich einfache Elastizitätsprobleme lösen lassen.This thesis mainly deals with the Green’s function for linear generally anisotropic materials in the infinite three-dimensional space, also called the fundamental solution. The detailed derivations and the numerical results of the explicit expressions of the Green’s function and its first and second derivatives based on the residue calculus method (RCM), Stroh formalism method (SFM) and unified explicit expression method (UEEM) are presented. The numerical examples of the three different methods are compared with each other for the anisotropic elasticity. All three methods are accurate for an arbitrary point in non-degenerate cases. For nearly degenerate cases, both the RCM and the SFM become unstable while the UEEM keeps accurate. Moreover, the SFM is more stable than the RCM. To overcome the difficulty in nearly degenerate cases and degenerate cases, some material constants are slightly changed in the RCM and the SFM. Although the UEEM has some advantages compared with the RCM and the SFM, it is difficult to be extended to the multifield coupled materials. The RCM and SFM are extended to the piezoelectric materials and compared with each other. Since the SFM has a better performance than the RCM for the piezoelectric materials, it is extended further to the magnetoelectroelastic materials. The UEEM is implemented into a Boundary Element Method (BEM) as an application. Some demonstrative anisotropic elastic problems are solved by the developed BEM

An accurate beam theory and its first-order approximation in free vibration analysis

An infinite system of one-dimensional differential equations is derived from the two-dimensional theory of elasticity by expanding the displacement field in a series of trigonometrical functions together with a linear term. Since the trigonometrical functions are pure thickness-vibration modes of infinite plates or beams with the top and bottom surfaces being free, the differential equations and the corresponding boundary conditions serve as the basis of an accurate beam theory for vibration analysis, named Lee's beam theory (LBT). Naturally, a high-order set of the infinite system should be quite useful in the analysis of beams at high frequencies. With the objective of vibration analysis of beams, this paper focuses on the first-order approximation, which leads to a first-order shear deformation beam theory for flexural vibrations (LBT1st). The differential equations in LBT1st are equivalent to those in Timoshenko's beam theory (TBT). The most important difference between LBT1st and TBT is the different field displacements. For the assessment of the accuracy of LBT1st, the numerical results of frequencies of free vibrations, frequency spectra and mode shapes of beams with classical boundary conditions are obtained and compared with those by TBT and plane stress problem of elasticity. Considering the plane stress problem as a reference, LBT1st is slightly more accurate in describing the field shapes of beams than TBT. Therefore, LBT1st, as well as LBT, is an addition to the existing beam theories with improved accuracy for the vibration analysis of beams and their combinations

Analysis of Vibration Frequencies of Piezoelectric Ceramic Rings as Ultrasonic Transducers in Welding of Facial Mask Production

The explosive demands for facial masks as vital personal protection equipment (PPE) in the wake of Covid-19 have challenged many industries and enterprises in technology and capacity, and the piezoelectric ceramic (PZT) transducers for the production of facial masks in the welding process are in heavy demand. In the earlier days of the epidemic, the supply of ceramic transducers cannot meet its increasing demands, and efforts in materials, development, and production are mobilized to provide the transducers to mask producers for quick production. The simplest solution is presented with the employment of Rayleigh-Ritz method for the vibration analysis, then different materials can be selected to achieve the required frequency and energy standards. The fully tailored method and results can be utilized by the engineers for quick development of the PZT transducers to perform precise function in welding

Spatial–Temporal Evolution and Regional Differentiation Features of Urbanization in China from 2003 to 2013

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

CUEDC2 Drives β-Catenin Nuclear Translocation and Promotes Triple-Negative Breast Cancer Tumorigenesis

Hyperactivation of Wnt signaling is crucial in tumor formation. Fully elucidating the molecular details of how the cancer-specific Wnt signaling pathway is activated or contributes to tumorigenesis will help in determining future treatment strategies. Here, we aimed to explore the contribution of CUEDC2, a novel CUE-domain-containing protein, to the activation of Wnt signaling and the tumorigenesis of triple-negative breast cancer (TNBC) and to determine the underlying mechanisms. TNBC patient samples and disease-free survival (DFS) data were used to determine the association between CUEDC2 and TNBC progression. The effects of CUEDC2 on TNBC were examined in TNBC cells in vitro and in subcutaneous xenograft tumors in vivo. Gene knockdown, immunoprecipitation plus liquid chromatography–tandem mass spectrometry, pull-down, co-immunoprecipitation, localized surface plasmon resonance, and nuclear translocation analysis were used to uncover the mechanisms of CUEDC2 in regulating Wnt signaling and TNBC development. CUEDC2 is sufficient to maintain the hyperactivation of Wnt signaling required for TNBC tumorigenesis. The contribution of CUEDC2 plays a major role in determining the outcome of oncogenic Wnt signaling both in vitro and in vivo. Mechanistically, the CUE domain in CUEDC2 directly bound to the ARM (7–9) domain in β-catenin, promoted β-catenin nuclear translocation and enhanced the expression of β-catenin targeted genes. More importantly, an 11-amino-acid competitive peptide targeting the CUE domain in CUEDC2 blocked the interactions of CUEDC2 and β-catenin and abrogated the malignant phenotype of TNBC cells in vitro and in vivo. We observed that TNBC patients who exhibited higher levels of CUEDC2 showed marked hyperactivation of the Wnt signaling pathway and poor clinical outcomes, highlighting the clinical relevance of our findings. CUEDC2 promotes TNBC tumor growth by enhancing Wnt signaling through directly binding to β-catenin and accelerating its nuclear translocation. Targeting the interactions of CUEDC2 and β-catenin may be a valuable strategy for combating TNBC