Integration of finite element modeling with solid modeling through a dynamic interface

Finite element modeling is dominated by geometric modeling type operations. Therefore, an effective interface to geometric modeling requires access to both the model and the modeling functionality used to create it. The use of a dynamic interface that addresses these needs through the use of boundary data structures and geometric operators is discussed

Numerično modeliranje dendritskega strjevanja na podlagi formulacije faznega polja in prilagodljivega brezmrežnega rešitvenega postopka

The main aim of the dissertation is to develop a novel numerical approach for an accurate and computationally efficient modelling of dendritic solidification, which is one of the most commonly observed phenomena in the industrial casting of the metallic alloys. The size and the morphology of dendritic structures as well as the distribution of the solute within them critically effect the mechanical and the electro-chemical properties of the solidified material. The numerical modelling of dendritic solidification can be applied for an in-depth understanding and optimisation of the casting process under various solidification conditions and chemical compositions of the alloy under consideration. The dendritic solidification of pure materials and dilute multi-component alloys is considered in the dissertation. The phase field formulation is applied for the modelling of dendritic solidification. The formulation is based on the introduction of the continuous phase field variable that is constant in the bulk of the solid and liquid phases. The phase field variable has a smooth transition from the value denoting the solid phase to the value denoting the liquid phase at the solid-liquid interface over the characteristic interface thickness. A phase field model yields a system of coupled non-linear parabolic partial differential equations that govern the evolution of the phase field and other thermodynamic variables. The meshless radial basis function-generated finite-differences (RBF-FD) method is used for the spatial discretisation of the system of partial differential equations. The forward Euler scheme is applied for the temporal discretisation. Fifth-degree polyharmonic splines are used as the shape functions in the RBF-FD method. A second-order accurate RBF-FD method is achieved by augmenting the shape functions with monomials up to the second degree. The adaptive solution procedure is developed in order to speed-up the calculations. The procedure is based on the quadtree domain decomposition of a rectangular computational domain into rectangular computational sub-domains of different sizes. Each quadtree sub-domain has its own regular or scattered distribution of computational nodes in which the RBF-FD method and the forward Euler scheme apply for the discretisation of the system of partial differential equations. The adaptive solution procedure dynamically ensures the prescribed highest density of the computational nodes at the solid-liquid interface and the lowest-possible density in the bulk of the solid and liquid phases. The adaptive time-stepping is employed to further speed-up the calculations. The stable time step in the forward Euler scheme depends on the density of the computational nodeshence, different time steps can be used in quadtree sub-domains with different node densities. The main originality of the present work is the use of the RBF-FD method for the thorough analysis of the impact of the type of the node distribution and the size of a local sub-domain to the accuracy when the phase field modelling of dendritic solidification for arbitrary preferential growth directions is considered. It is shown how the use of the scattered node distribution reduces the undesirable mesh-induced anisotropy effects, present when the partial differential equations are discretisied on a regular node distribution. The main advantage of the RBF-FD method for the phase field modelling of dendritic growth is the simple discretisation of the partial differential equations on the scattered node distributions. The RBF-FD method is, for the first time, used in combination with the spatial-temporal adaptive solution procedure based on the quadtree domain decomposition. The adaptive solution procedure successfully speeds-up the calculationshowever, the advantages of the use of the scattered node distribution are partly compromised due to the impact of regularity in the quadtree domain decomposition.Glavni cilj disertacije je razvoj novega numeričnega pristopa za natančno in računsko učinkovito modeliranje dendritskega strjevanja. Dendritsko strjevanje je eden najpogosteje opaženih pojavov pri industrijskem ulivanju kovinskih zlitin. Velikost in morfologija dendritskih struktur ter porazdelitev topljencev v njih ključno vplivajo na mehanske in elektro-kemijske lastnosti strjenega materiala. Numerično modeliranje dendritskega strjevanja se lahko uporablja za poglobljeno razumevanje in optimizacijo procesa ulivanja pri različnih pogojih strjevanja in pri različnih kemijskih sestavah obravnavane zlitine. V disertaciji obravnavamo dendritsko strjevanje čistih snovi in razredčenih več-sestavinskih zlitin. Za modeliranje dendritskega strjevanja uporabimo formulacija faznega polja. Formulacija temelji na uvedbi zvezne spremenljivke faznega polja, ki je konstantna v trdni in kapljeviti fazi. Spremenljivka faznega polja ima na medfaznem robu zvezen prehod preko značilne debeline medfaznega roba od vrednosti, ki označuje trdno fazo, do vrednosti, ki označuje kapljevito fazo. Model faznega polja poda sistem sklopljenih nelinearnih paraboličnih parcialnih diferencialnih enačb, ki opisujejo časovni razvoj faznega polja in ostalih termodinamskih spremenljivk. Za krajevno diskretizacijo sistema parcialnih diferencialnih enačb uporabimo brezmrežno metodo z radialnimi baznimi funkcijami generiranih končnih razlik (RBF-KR). Za časovno diskretizacijo uporabimo eksplicitno Eulerjevo shemo. Poliharmonične zlepke petega reda uporabimo kot oblikovne funkcije v metodi RBF-KR. Natančnost drugega reda metode RBF-KR dosežemo z dodajanjem monomov do vključno drugega reda k oblikovnim funkcijam. Za pospešitev izračunov razvijemo prilagodljiv rešitveni postopek. Postopek temelji na razdelitvi pravokotne računske domene na pravokotne računske pod-domene različnih velikosti z uporabo štiriškega drevesa. Vsaka pod-domena na štiriškem drevesu vsebuje svojo lastno regularno ali razmetano porazdelitev računskih točk, v katerih z uporabo metode RBF-KR in eksplicitne Eulerjeve sheme diskretiziramo sistem parcialnih diferencialnih enačb. Prilagodljiv rešitveni postopek dinamično zagotavlja predpisano najvišjo gostoto računskih točk na trdno-kapljevitem medfaznem robu in najmanjšo možno gostoto v notranjosti trdne in kapljevite faze. Za dodatno pohitritev izračunov uporabimo prilagodljivo časovno korakanje. Stabilen časovni korak v eksplicitni Eulerjevi shemi je odvisen od gostote računskih točk, zaradi česar lahko uporabimo različne časovne korake v pod-domenah štiriškega drevesa z različnimi gostotami točk. Glavna novost predstavljenega dela je v uporabi metode RBF-KR za temeljito analizo vpliva tipa porazdelitve računskih točk in velikosti lokalnih pod-domen na natančnost pri modeliranju dendritskega strjevanja pri poljubnih preferenčnih smereh rasti z uporabo metode faznega polja. Pokažemo, kako uporaba razmetanih računskih točk zmanjša neželjen vpliv mrežne anizotropije, ki je prisotna, kadar parcialne diferencialne enačbe diskretiziramo na regularni porazdelitvi računskih točk. Glavna prednost metode RBF-KR za modeliranje dendritskega strjevanja je preprosta diskretizacija parcialnih diferencialnih enačb na razmetanih porazdelitvah računskih točk. Metoda RBF-KR je prvič uporabljena v kombinaciji s krajevno-časovnim prilagodljivim rešitvenim postopkom, ki temelji na razdelitvi računske domene s štiriškim drevesom. Prilagodljiv rešitveni postopek uspešno pohitri izračune, vendar se prednosti uporabe razmetane porazdelitve računskih točk delno zmanjšajo zaradi vpliva regularnosti pri razdelitvi računske domene s štiriškim drevesom

An Automatic Level Set Based Liver Segmentation from MRI Data Sets

A fast and accurate liver segmentation method is a challenging work in medical image analysis area. Liver segmentation is an important process for computer-assisted diagnosis, pre-evaluation of liver transplantation and therapy planning of liver tumors. There are several advantages of magnetic resonance imaging such as free form ionizing radiation and good contrast visualization of soft tissue. Also, innovations in recent technology and image acquisition techniques have made magnetic resonance imaging a major tool in modern medicine. However, the use of magnetic resonance images for liver segmentation has been slow when we compare applications with the central nervous systems and musculoskeletal. The reasons are irregular shape, size and position of the liver, contrast agent effects and similarities of the gray values of neighbor organs. Therefore, in this study, we present a fully automatic liver segmentation method by using an approximation of the level set based contour evolution from T2 weighted magnetic resonance data sets. The method avoids solving partial differential equations and applies only integer operations with a two-cycle segmentation algorithm. The efficiency of the proposed approach is achieved by applying the algorithm to all slices with a constant number of iteration and performing the contour evolution without any user defined initial contour. The obtained results are evaluated with four different similarity measures and they show that the automatic segmentation approach gives successful results

Automatic 3D modeling by combining SBFEM and transfinite element shape functions

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed and each cubic cell is treated as an SBFEM subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with certain transition elements on the subdomains' surfaces. Thus, we avoid the triangulation of surfaces employed in previous works and consequently reduce the number of surface elements and degrees of freedom. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly

An Open Source, Autonomous, Vision-Based Algorithm for Hazard Detection and Avoidance for Celestial Body Landing

Planetary exploration is one of the main goals that humankind has established as a must for space exploration in order to be prepared for colonizing new places and provide scientific data for a better understanding of the formation of our solar system. In order to provide a safe approach, several safety measures must be undertaken to guarantee not only the success of the mission but also the safety of the crew. One of these safety measures is the Autonomous Hazard, Detection, and Avoidance (HDA) sub-system for celestial body landers that will enable different spacecraft to complete solar system exploration. The main objective of the HDA sub-system is to assemble a map of the local terrain during the descent of the spacecraft so that a safe landing site can be marked down. This thesis will be focused on a passive method using a monocular camera as its primary detection sensor due to its form factor and weight, which enables its implementation alongside the proposed HDA algorithm in the Intuitive Machines lunar lander NOVA-C as part of the Commercial Lunar Payload Services technological demonstration in 2021 for the NASA Artemis program to take humans back to the moon. This algorithm is implemented by including two different sources for making decisions, a two-dimensional (2D) vision-based HDA map and a three-dimensional (3D) HDA map obtained through a Structure from Motion process in combination with a plane fitting sequence. These two maps will provide different metrics in order to provide the lander a better probability of performing a safe touchdown. These metrics are processed to optimize a cost function

Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami

The 11 March 2011 Tohoku tsunami is simulated using the quadtree-adaptive Saint-Venant solver implemented within the Gerris Flow Solver. The spatial resolution is adapted dynamically from 250 m in flooded areas up to 250 km for the areas at rest. Wave fronts are tracked at a resolution of 1.8 km in deep water. The simulation domain extends over 73° of both latitude and longitude and covers a significant part of the north-west Pacific. The initial wave elevation is obtained from a source model derived using seismic data only. Accurate long-distance wave prediction is demonstrated through comparison with DART buoys timeseries and GLOSS tide gauges records. The model also accurately predicts fine-scale flooding compared to both satellite and survey data. Adaptive mesh refinement leads to orders-of-magnitude gains in computational efficiency compared to non-adaptive methods. The study confirms that consistent source models for tsunami initiation can be obtained from seismic data only. However, while the observed extreme wave elevations are reproduced by the model, they are located further south than in the surveyed data. Comparisons with inshore wave buoys data indicate that this may be due to an incomplete understanding of the local wave generation mechanisms

An Approach to Improve Multi objective Path Planning for Mobile Robot Navigation using the Novel Quadrant Selection Method

Currently, automated and semi-automated industries need multiple objective path planning algorithms for mobile robot applications. The multi-objective optimisation algorithm takes more computational effort to provide optimal solutions. The proposed grid-based multi-objective global path planning algorithm [Quadrant selection algorithm (QSA)] plans the path by considering the direction of movements from starting position to the target position with minimum computational effort. Primarily, in this algorithm, the direction of movements is classified into quadrants. Based on the selection of the quadrant, the optimal paths are identified. In obstacle avoidance, the generated feasible paths are evaluated by the cumulative path distance travelled, and the cumulative angle turned to attain an optimal path. Finally, to ease the robot’s navigation, the obtained optimal path is further smoothed to avoid sharp turns and reduce the distance. The proposed QSA in total reduces the unnecessary search for paths in other quadrants. The developed algorithm is tested in different environments and compared with the existing algorithms based on the number of cells examined to obtain the optimal path. Unlike other algorithms, the proposed QSA provides an optimal path by dramatically reducing the number of cells examined. The experimental verification of the proposed QSA shows that the solution is practically implementable

An Optimization Based Design Framework for Multi-Functional 3D Printing

This work investigates design analysis and optimization methods for the integration of active internal systems into a component for manufacture using multi-material 3D printing processes. This enables efficient design of optimal multifunctional components that exploit the design freedoms of additive manufacturing (AM). The main contributions of this paper are in two areas: 1) the automated placement and routing of electrical systems within the component volume and, 2) the accommodation of the effect of this system integration on the structural response of the part through structural topology optimization (TO). A novel voxel modeling approach was used to facilitate design flexibility and to allow direct mapping to the 3D printer jetting nozzles.Mechanical Engineerin