An Integral Equation Approach For The Solution Of The Stokes Flow With Hermite Surface

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Üç boyutlu Stokes akışını çözmek amacıyla sınır integral yöntemiyle beraber dörtgen Hermit yüzeyler kullanılarak bir integral denklem yöntemi geliştirilmiştir. Sayısal sonuçlar, sınır sıralama yönteminden ve daimi Stokes denkleminin temel çözümleri olan Stokesletlerin sürekli dağılımından yararlanılarak elde edilmiştir. Dörtgen yüzey elemanları, komşu elemanlar arasındaki yüzey normal vektörünün sürekliliğini sağlayan hermite fonksiyonları kullanılarak tanımlanmıştır. Tekil integraller tanh-sinh tümlev yöntemi, tekil olmayan integraller ise Gauss-Legendre yöntemi kullanılarak sayısal olarak hesaplanmıştır. Sayısal algoritma ilk olarak küre etrafindaki üç boyutlu Stokes akışında doğrulanmıştır. Sonrasında algoritma küresel parçacıkların sedimantasyonu problemi için uygulanmıştır.An integral equation method has been developed to solve the three-dimensional Stokes flow using a quadrilateral Hermite based function approach to the boundary integral method. The numerical solutions are obtained by utilizing the boundary collocation method as well as the continuous distribution of Stokeslets, which are the fundamental solutions of the steady Stokes equations. The quadrilateral surface elements are based on the bi-cubic hermite functions that allows the continuous variation of the surface normal vectors between neighboring elements. The singular integrations are evaluated numerically using the tanh-sinh quadrature rule meanwhile non-singular integrals are evaluated using the Gauss-Legendre quadrature rule. The numerical algorithm is initially validated for the three-dimensional unbounded Stokes flow around a sphere. Then the algorithm is applied to the sedimentation of spherical particles. Keywords: Integral equation method, Stokes flow, Hermite functions, singular integrals, sedimentation

Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.Comment: 14 pages, 8 figures and 96 references. Revised version resubmitted to Phys. Fluid

Post-Earthquake Structural Damage Assessment Through Point Cloud Data

Structural damage assessment following an extreme event can provide valuable information and insight into unanticipated damage and failure modes to improve design philosophies and design codes as well as reduce vulnerability. Oftentimes, structural engineers create finite element models (FEM) of the structure in which numerous model parameters require calibration to simulate the current state. This information may include structural plan details (geometry), material characteristics (strength and stiffness parameters), as well as observed damage patterns (cracks, spalling, etc.). Ground-based lidar (GBL) scans and Structure-from-Motion (SfM) can rapidly capture dimensionally accurate point clouds of the structure or facility of interest. Furthermore, point clouds can used to efficiently document perishable structural damage data digitally prior recovery or retrofit efforts. Within these point clouds, information can be extracted to objectively locate damage patterns in non-temporal datasets. Localization and quantification of damage can serve to update models with high fidelity within forensic investigations as well as to estimate the remaining structural capacity. In this work, an algorithm based on two spatially invariant geometrical features was used to identify and quantify structural damage from point cloud data for two case study buildings. The first case-study building is an 18-story high-rise condominium building that was significantly damaged during the 2015 Gorkha (Nepal) Earthquake. The damage included significant cracks in partition walls, unreinforced masonry infill walls, and section-loss within coupling beams and staircases at various levels. The second case-study structure, from the same earthquake event, is a five-tiered pagoda style temple built using timber beams and thick brick masonry walls. The temple sustained moderate damage where shear cracks developed at lower levels and seam of the wall piers. Through the developed damage detection method, cracking, concrete spalling, and loss of cross-section within the point cloud data of the nonstructural and structural elements are quantified

Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity

We preset a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and evaluate and extend four well established schemes for their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, J\"ulicher 1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6, 1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer, p35, termed A, B, C, D. We present a comparative study of these four schemes on the minimal bending model and propose extensions for schemes B, C and D. These extensions incorporate the reference state and non-local energy to account for the spontaneous curvature, bilayer coupling, and area-difference elasticity models. Our results indicate that the proposed extensions enhance the models to account for shape transformation including budding/vesiculation as well as for non-axisymmetric shapes. We find that the extended scheme B is superior to the rest in terms of accuracy, and robustness as well as simplicity of implementation. We demonstrate the capabilities of this scheme on several benchmark problems including the budding-vesiculating process and the reproduction of the phase diagram of vesicles

Structural Identification of an 18-Story RC Building in Nepal Using Post-Earthquake Ambient Vibration and Lidar Data

Few studies have been conducted to systematically assess post-earthquake condition of structures using vibration measurements. This paper presents system identification and finite element (FE) modeling of an 18-story apartment building that was damaged during the 2015 Gorkha earthquake and its aftershocks in Nepal. In June 2015, a few months after the earthquake, the authors visited the building and recorded the building’s ambient acceleration response. The recorded data are analyzed, and the modal parameters of the structure are identified using an output-only system identification method. A linear FE model of the building is also developed to estimate numerically its dynamic properties. The identified modal parameters are compared to those of the model to identify possible shortcomings of the modeling and identification approaches. The identified natural frequencies and mode shapes for two of the three closely spaced vibration modes in the lower frequency range of interest (0.2–1.0 Hz) are in good agreement with the numerical model. The model is used to estimate the response of the building to the nearby recorded ground motion due to earthquake and the main aftershock. The maximum drift ratios are compared to the observed damage in the building and surface defects detected and quantified by the lidar scans as the research team performed a series of light detection and ranging (lidar) scans from interior of selected floors to document the damage patterns along the height of the building