scholarly journals Fully and semi-automated shape differentiation in NGSolve

2020 ◽  
Author(s):  
Peter Gangl ◽  
Kevin Sturm ◽  
Michael Neunteufel ◽  
Joachim Schöberl
Keyword(s):  
Nonlinear Problems ◽  
Automatic Generation ◽  
Second Order ◽  
Shape Optimisation ◽  
Finite Element Software ◽  
Unconstrained Model ◽  
Taylor Test ◽  
Different Types ◽  
Numerical Optimisation ◽  
Shape Differentiation

Abstract In this paper, we present a framework for automated shape differentiation in the finite element software . Our approach combines the mathematical Lagrangian approach for differentiating PDE-constrained shape functions with the automated differentiation capabilities of . The user can decide which degree of automatisation is required, thus allowing for either a more custom-like or black-box–like behaviour of the software. We discuss the automatic generation of first- and second-order shape derivatives for unconstrained model problems as well as for more realistic problems that are constrained by different types of partial differential equations. We consider linear as well as nonlinear problems and also problems which are posed on surfaces. In numerical experiments, we verify the accuracy of the computed derivatives via a Taylor test. Finally, we present first- and second-order shape optimisation algorithms and illustrate them for several numerical optimisation examples ranging from nonlinear elasticity to Maxwell’s equations.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

Quantitative Models of Motor Responses Subject to Longitudinal, Lateral, and Preview Constraints

1978 ◽  
Vol 20 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Motor Control ◽  
Linear Models ◽  
Movement Time ◽  
Arm Movements ◽  
Second Order ◽  
Motor Responses ◽  
First Order ◽  
Different Types ◽  
Index Of Difficulty

First- and second-order linear models of mean movement time for serial arm movements aimed at a target and subject to preview constraints and lateral constraints were formulated as extensions of the so-called Fitts's law of motor control. These models were validated on the basis of experimental data from five subjects and found to explain from 80% to 85% of the variation in movement time in the case of the first-order models and from 93% to 95% of such variation for the second-order models. Fitts's index of difficulty (ID) was generally found to contribute more to the movement time than did either the preview ID or the lateral ID defined. Of the different types of errors, target overshoots occurred far more frequently than undershoots.

scholarly journals Dye removal abilities of the mesophilic and thermophilic biomass: a kinetics study

2018 ◽  
Vol 20 (2) ◽  
pp. 408-416
Keyword(s):  
Intraparticle Diffusion ◽  
Second Order ◽  
Intraparticle Diffusion Model ◽  
First Order Kinetics ◽  
Different Types ◽  
Pseudo Second Order ◽  
Acidic Conditions ◽  
Red Dye ◽  
Experimental Kinetics ◽  
Kinetics Of

Mesophilic biomass and thermophilic biomass samples were isolated and used to remove Dorasyn Red dye from aqueous solutions. The biosorption kinetics of dye uptake by four different types of biomass at three temperatures (20, 30, and 40 °C) were investigated using pseudo-first order kinetics, pseudo-second order kinetics, intraparticle diffusion, Elovich, and Bangham models. The pseudo-second-order kinetics model and the first stage of the intraparticle diffusion model were effective in describing the experimental kinetics data. The biosorption results showed that the mesophilic biomass samples could be useful for removing dye under acidic conditions.

scholarly journals Finite Element Software for Rubber Products Design

2018 ◽  
Vol 3 (1) ◽  
pp. 13-20
Author(s):  
Dávid Huri
Keyword(s):  
Finite Element ◽  
Complex Analysis ◽  
Large Deformations ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Material Models ◽  
Finite Element Software ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Different Types

Automotive rubber products are subjected to large deformations during working conditions, they often contact with other parts and they show highly nonlinear material behavior. Using finite element software for complex analysis of rubber parts can be a good way, although it has to contain special modules. Different types of rubber materials require the curve fitting possibility and the wide range choice of the material models. It is also important to be able to describe the viscoelastic property and the hysteresis. The remeshing possibility can be a useful tool for large deformation and the working circumstances require the contact and self contact ability as well. This article compares some types of the finite element software available on the market based on the above mentioned features.

scholarly journals Cross-disciplinary Science and the Structure of Scientific Perspectives

2014 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Hugo Fjelsted Alrøe ◽  
Egon Noe
Keyword(s):  
Nature Of Science ◽  
Real World ◽  
Scientific Research ◽  
Second Order ◽  
Philosophical Analysis ◽  
Different Types ◽  
Real World Problems

<p>Cross-disciplinary use of science is needed to solve complex, real-world problems, but carrying out scientific research with multiple very different disciplines is in itself a non-trivial problem. Perspectives matter. In this paper we carry out a philosophical analysis of the perspectival nature of science, focusing on the synchronic structure of scientific perspectives across disciplines and not on the diachronic, historical structure of shifting perspectives within single disciplines that has been widely discussed since Kuhn and Feyerabend. We show what kinds of cross-disciplinary disagreement to expect due to the perspectival structure of science, suggest how to handle different scientific perspectives in cross-disciplinary work through perspectives of a second order, and discuss some fundamental epistemic differences between different types of science.</p>

Influence of imperfections on the stiffness of regular scaffold structures

2016 ◽  
Vol 232 (6) ◽  
pp. 453-464
Author(s):  
Ainhoa Martinez Ormaetxea ◽  
Andreas Öchsner
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Programming Language ◽  
Manufacturing Process ◽  
Experimental Testing ◽  
Bone Scaffold ◽  
Finite Element Software ◽  
Different Types ◽  
Data Files ◽  
Load Conditions

The manufacturing process of bone scaffold structures has an important influence on the final mechanical strength of the structure. When the structures are not produced properly, i.e. have imperfections such as missing parts or slightly displaced joints, they lose some of their mechanical properties. The aim of this study was to see how different types of damage affect the structures and also if their effects are equal when the structure is subjected to different load conditions. The change of the mechanical behavior was determined using the commercial finite element software MSC Marc Mentat. In turn, the damage was introduced by manipulating the structure’s files (ASCII data files) using the programming language Fortran. Apart from the numerical simulations, experimental testing was also performed to verify the numerical results. In the frame of this study, useful information for further research is provided.

Simplified Analysis of Second-Order Effect on Staggered Truss Structure

2012 ◽  
Vol 446-449 ◽  
pp. 857-862
Author(s):  
Qi Shi Zhou ◽  
Xu Hong Zhou ◽  
Li Ming Yang
Keyword(s):  
Structural Characteristics ◽  
Order Effect ◽  
Second Order ◽  
Truss Structure ◽  
Order Effects ◽  
Good Precision ◽  
Finite Element Software ◽  
Load Carrying ◽  
Second Order Effects ◽  
Lateral Displacements

Based on the structural characteristics that the distribution of mass and stiffness is symmetrical in staggered truss structure, the load-carrying performance of staggered truss structure is equivalent to a pressure-bend combinational strut in this paper. By analyzing the relationship among curvatures , bending moments and shear forces of the pressure-bend combinational strut, the balance differential equations of the pressure-bend combinational strut is erected. Based on Runge-Kutta method, the lateral iteration equation derived by considering the influence of the second-order effects is derived. This paper analyzes the lateral displacements of floors of the staggered truss structure examples considering second-order effects or not, and gives a comparative analysis with the existing finite element software Ansys. The results show that the calculation method of second-order effects proposed in this paper has a good precision.

Coherence of subsumption, minimum typing and type-checking in F ≤

1992 ◽  
Vol 2 (1) ◽  
pp. 55-91 ◽  
Author(s):  
Pierre-Louis Curien ◽  
Giorgio Ghelli
Keyword(s):  
Normal Form ◽  
Type System ◽  
Lambda Calculus ◽  
Complete Information ◽  
Second Order ◽  
Semantic Interpretation ◽  
Type Checking ◽  
Rewriting System ◽  
Different Types ◽  
Rewriting Rules

A subtyping relation ≤ between types is often accompanied by a typing rule, called subsumption: if a term a has type T and T≤U, then a has type U. In presence of subsumption, a well-typed term does not codify its proof of well typing. Since a semantic interpretation is most naturally defined by induction on the structure of typing proofs, a problem of coherence arises: different typing proofs of the same term must have related meanings. We propose a proof-theoretical, rewriting approach to this problem. We focus on F≤, a second-order lambda calculus with bounded quantification, which is rich enough to make the problem interesting. We define a normalizing rewriting system on proofs, which transforms different proofs of the same typing judgement into a unique normal proof, with the further property that all the normal proofs assigning different types to a given term in a given environment differ only by a final application of the subsumption rule. This rewriting system is not defined on the proofs themselves but on the terms of an auxiliary type system, in which the terms carry complete information about their typing proof. This technique gives us three different results:— Any semantic interpretation is coherent if and only if our rewriting rules are satisfied as equations.— We obtain a proof of the existence of a minimum type for each term in a given environment.— From an analysis of the shape of normal form proofs, we obtain a deterministic typechecking algorithm, which is sound and complete by construction.

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