Search results for: spacetime singularity

Authors: Ming-Hsiang Shih, Wen-Pei Sung, Shih-Heng Tung

Abstract:

The purposes of hydraulic gate are to maintain the functions of storing and draining water. It bears long-term hydraulic pressure and earthquake force and is very important for reservoir and waterpower plant. The high tensile strength of steel plate is used as constructional material of hydraulic gate. The cracks and rusts, induced by the defects of material, bad construction and seismic excitation and under water respectively, thus, the mechanics phenomena of gate with crack are probing into the cause of stress concentration, induced high crack increase rate, affect the safety and usage of hydroelectric power plant. Stress distribution analysis is a very important and essential surveying technique to analyze bi-material and singular point problems. The finite difference infinitely small element method has been demonstrated, suitable for analyzing the buckling phenomena of welding seam and steel plate with crack. Especially, this method can easily analyze the singularity of kink crack. Nevertheless, the construction form and deformation shape of some gates are three-dimensional system. Therefore, the three-dimensional Digital Image Correlation (DIC) has been developed and applied to analyze the strain variation of steel plate with crack at weld joint. The proposed Digital image correlation (DIC) technique is an only non-contact method for measuring the variation of test object. According to rapid development of digital camera, the cost of this digital image correlation technique has been reduced. Otherwise, this DIC method provides with the advantages of widely practical application of indoor test and field test without the restriction on the size of test object. Thus, the research purpose of this research is to develop and apply this technique to monitor mechanics crack variations of weld steel hydraulic gate and its conformation under action of loading. The imagines can be picked from real time monitoring process to analyze the strain change of each loading stage. The proposed 3-Dimensional digital image correlation method, developed in the study, is applied to analyze the post-buckling phenomenon and buckling tendency of welded steel plate with crack. Then, the stress intensity of 3-dimensional analysis of different materials and enhanced materials in steel plate has been analyzed in this paper. The test results show that this proposed three-dimensional DIC method can precisely detect the crack variation of welded steel plate under different loading stages. Especially, this proposed DIC method can detect and identify the crack position and the other flaws of the welded steel plate that the traditional test methods hardly detect these kind phenomena. Therefore, this proposed three-dimensional DIC method can apply to observe the mechanics phenomena of composite materials subjected to loading and operating.

Keywords: welded steel plate, crack variation, three-dimensional digital image correlation (DIC), crack stel plate

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Authors: Simone Dell'Agnello

Abstract:

There are laser retroreflectors on the Moon and no laser retroreflectors on Mars. Here we describe the design, construction, qualification and imminent deployment of next-generation, optimized laser retroreflectors on the Moon and on Mars (where they will be the first ones). These instruments are positioned by time-of-flight measurements of short laser pulses, the so-called 'laser ranging' technique. Data analysis is carried out with PEP, the Planetary Ephemeris Program of CfA (Center for Astrophysics). Since 1969 Lunar Laser Ranging (LLR) to Apollo/Lunokhod laser retro-reflector (CCR) arrays supplied accurate tests of General Relativity (GR) and new gravitational physics: possible changes of the gravitational constant Gdot/G, weak and strong equivalence principle, gravitational self-energy (Parametrized Post Newtonian parameter beta), geodetic precession, inverse-square force-law; it can also constraint gravitomagnetism. Some of these measurements also allowed for testing extensions of GR, including spacetime torsion, non-minimally coupled gravity. LLR has also provides significant information on the composition of the deep interior of the Moon. In fact, LLR first provided evidence of the existence of a fluid component of the deep lunar interior. In 1969 CCR arrays contributed a negligible fraction of the LLR error budget. Since laser station range accuracy improved by more than a factor 100, now, because of lunar librations, current array dominate the error due to their multi-CCR geometry. We developed a next-generation, single, large CCR, MoonLIGHT (Moon Laser Instrumentation for General relativity high-accuracy test) unaffected by librations that supports an improvement of the space segment of the LLR accuracy up to a factor 100. INFN also developed INRRI (INstrument for landing-Roving laser Retro-reflector Investigations), a microreflector to be laser-ranged by orbiters. Their performance is characterized at the SCF_Lab (Satellite/lunar laser ranging Characterization Facilities Lab, INFN-LNF, Frascati, Italy) for their deployment on the lunar surface or the cislunar space. They will be used to accurately position landers, rovers, hoppers, orbiters of Google Lunar X Prize and space agency missions, thanks to LLR observations from station of the International Laser Ranging Service in the USA, in France and in Italy. INRRI was launched in 2016 with the ESA mission ExoMars (Exobiology on Mars) EDM (Entry, descent and landing Demonstration Module), deployed on the Schiaparelli lander and is proposed for the ExoMars 2020 Rover. Based on an agreement between NASA and ASI (Agenzia Spaziale Italiana), another microreflector, LaRRI (Laser Retro-Reflector for InSight), was delivered to JPL (Jet Propulsion Laboratory) and integrated on NASA’s InSight Mars Lander in August 2017 (launch scheduled in May 2018). Another microreflector, LaRA (Laser Retro-reflector Array) will be delivered to JPL for deployment on the NASA Mars 2020 Rover. The first lunar landing opportunities will be from early 2018 (with TeamIndus) to late 2018 with commercial missions, followed by opportunities with space agency missions, including the proposed deployment of MoonLIGHT and INRRI on NASA’s Resource Prospectors and its evolutions. In conclusion, we will extend significantly the CCR Lunar Geophysical Network and populate the Mars Geophysical Network. These networks will enable very significantly improved tests of GR.

Keywords: general relativity, laser retroreflectors, lunar laser ranging, Mars geodesy

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Authors: Adrian W. Egger, Savvas P. Triantafyllou, Eleni N. Chatzi

Abstract:

The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which introduces a scaling center in each element’s domain, thus transitioning from a Cartesian reference frame to one resembling polar coordinates. Consequently, an analytical solution is achieved in radial direction, implying that only the boundary need be discretized. The only limitation imposed on the resulting polygonal elements is that they remain star-convex. Further arbitrary p- or h-refinement may be applied locally in a mesh. The polygonal nature of SBFEM elements has been exploited in quadtree meshes to alleviate all issues conventionally associated with hanging nodes. Furthermore, since in 2D this results in only 16 possible cell configurations, these are precomputed in order to accelerate the forward analysis significantly. Any cells, which are clipped to accommodate the domain geometry, must be computed conventionally. However, since SBFEM permits polygonal elements, significantly coarser meshes at comparable accuracy levels are obtained when compared with conventional quadtree analysis, further increasing the computational efficiency of this scheme. The generalized stress intensity factors (gSIFs) are computed by exploiting the semi-analytical solution in radial direction. This is initiated by placing the scaling center of the element containing the crack at the crack tip. Taking an analytical limit of this element’s stress field as it approaches the crack tip, delivers an expression for the singular stress field. By applying the problem specific boundary conditions, the geometry correction factor is obtained, and the gSIFs are then evaluated based on their formal definition. Since the SBFEM solution is constructed as a power series, not unlike mode superposition in FEM, the two modes contributing to the singular response of the element can be easily identified in post-processing. Compared to the extended finite element method (XFEM) this approach is highly convenient, since neither enrichment terms nor a priori knowledge of the singularity is required. Computation of the gSIFs by SBFEM permits exceptional accuracy, however, when combined with hybrid quadtrees employing linear elements, this does not always hold. Nevertheless, it has been shown that crack propagation schemes are highly effective even given very coarse discretization since they only rely on the ratio of mode one to mode two gSIFs. The absolute values of the gSIFs may still be subject to large errors. Hence, we propose a post-processing scheme, which minimizes the error resulting from the approximation space of the cracked element, thus limiting the error in the gSIFs to the discretization error of the quadtree mesh. This is achieved by h- and/or p-refinement of the cracked element, which elevates the amount of modes present in the solution. The resulting numerical description of the element is highly accurate, with the main error source now stemming from its boundary displacement solution. Numerical examples show that this post-processing procedure can significantly improve the accuracy of the computed gSIFs with negligible computational cost even on coarse meshes resulting from hybrid quadtrees.

Keywords: linear elastic fracture mechanics, generalized stress intensity factors, scaled finite element method, hybrid quadtrees

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