scholarly journals Finding three-dimensional layouts for crashworthiness load cases using the graph and heuristic based topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 59-73
Author(s):  
F. Beyer ◽  
D. Schneider ◽  
A. Schumacher
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Expert Knowledge ◽  
Three Dimensional ◽  
Mathematical Optimization ◽  
Frame Structure ◽  
Two Dimensional ◽  
Structural Components ◽  
Maximal Contact ◽  
Dimensional Graph

AbstractIn this paper we present a new procedure using the graph and heuristic based topology optimization in order to find layouts for three-dimensional frame structures under crash loads. A three-dimensional graph describes the geometry and is used to derive a finite element shell model. The model of the frame structure consists of different profiles with continuous cross-sections. The ends of the profiles are currently rigidly connected. Each cross-section is defined by an individual two-dimensional graph. After performing a simulation its results are used by competing heuristics to propose new topologies for the frame structure. Most of these heuristics are derived from expert knowledge. Over several iterations, the goal is to improve the structures mechanical behavior. Typical objectives are the minimization of the structural intrusion in a crash scenario or the minimization of the maximal contact force between structural components. The presented method includes topology optimization by heuristics and shape optimization respectively sizing by mathematical optimization algorithms. The new flexible syntax for three- and two-dimensional graphs, the optimization process and the currently used heuristics are described. The performance is demonstrated for two examples, each optimized twice with opposing objectives.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

scholarly journals A New Approach to Accuracy Evaluation of Single-Tooth Abutment Using Two-Dimensional Analysis in Two Intraoral Scanners

2019 ◽  
Vol 16 (6) ◽  
pp. 1021 ◽  
Author(s):  
Jiyoun Maeng ◽  
Young-Jun Lim ◽  
Bongju Kim ◽  
Myung-Joo Kim ◽  
Ho-Beom Kwon
Keyword(s):  
Dimensional Analysis ◽  
Cross Sections ◽  
Three Dimensional ◽  
Accuracy Evaluation ◽  
Two Dimensional ◽  
3D Data ◽  
Accuracy Comparison ◽  
Single Tooth ◽  
Sharp Edges ◽  
Data Files

The aim of this study was to two-dimensionally evaluate deviation errors at five digital cross-sections of single-tooth abutment in regards to data obtained from two intraoral scanners, and to evaluate accuracy of individual scanners. Two intraoral scanners, the Trios 3® (3 Shape, Copenhagen, Denmark) and EzScan® (Vatech, Hwaseong, Korea), were evaluated by utilizing 13 stone models. The superimposed 3D data files were sectioned into five different planes: buccal-lingual section (BL), mesial-distal section (MD), transverse high section (TH), transverse middle section (TM), and transverse low section (TL). Accuracy comparison between the two scanners in 5 groups was performed. BL vs. MD of each scanner, and three transverse groups (TH, TM, TL) of each scanner were analyzed for accuracy comparison. In comparison of 2-D analyses for two intraoral scanners, Trios 3® showed statistically significant higher accuracy in root mean square (RMS) at BL, TH, and TL (p < 0.05). For each scanner, RMS value showed that mesial-distal sections were more prone to error than buccal-lingual section, which exhibited statistically significant errors (p < 0.05) while the transverse groups did not. Two-dimensional analysis is more insightful than three-dimensional analysis on single-tooth abutment. In mesiodistal areas, rough prepped areas, and sharp edges where scanner accessibility is difficult, high deviation errors are shown.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

scholarly journals Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

2017 ◽  
Vol 14 (135) ◽  
pp. 20170635 ◽  
Author(s):  
B. Zeller-Plumhoff ◽  
K. R. Daly ◽  
G. F. Clough ◽  
P. Schneider ◽  
T. Roose
Keyword(s):  
Skeletal Muscle ◽  
Muscle Tissue ◽  
Cross Sections ◽  
Tissue Oxygenation ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Capillary Density ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Contrast Imaging

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

Gravitational attraction of a rectangular prism with depth‐dependent density

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 470-473 ◽  
Author(s):  
J. García‐Abdeslem
Keyword(s):  
Cross Sections ◽  
Integral Method ◽  
Three Dimensional ◽  
Density Contrast ◽  
Gravitational Attraction ◽  
Two Dimensional ◽  
Gravity Effect ◽  
Line Integral ◽  
Closed Expression ◽  
Dependent Density

The gravity effect produced by two and three‐dimensional bodies with nonuniform density contrast has been treated by several authors. One of the first attempts in this direction made by Cordell (1973), who developed a method to compute the gravity effect due to a two‐dimensional prism whose density decreases exponentially with depth. A different approach was proposed by Murthy and Rao (1979). They extended the line‐integral method to obtain the gravity effect for bodies of arbitrary cross‐sections, with density contrast varying linearly with depth. Chai and Hinze (1988) have derived a wavenumber‐domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth. Recently, Rao (1990) has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial.

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