Evaluation of Error Bounds in an Optimization Problem Using the Finite-Element Method

1974 ◽  
Vol 41 (1) ◽  
pp. 269-272 ◽  
Author(s):  
E. M. Buturla ◽  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Optimization Problem ◽  
The Finite Element Method ◽  
Numerical Convergence ◽  
Optimization Study ◽  
Approximation Errors ◽  
Analytical Development ◽  
Circular Disks

Results of a numerical analysis completed in conjunction with the analytical development of a previous work are presented. The problem is an optimization study involving the thermal deflections of two parallel circular disks. The capability of choosing a mesh refinement to arbitrarily reduce approximation errors is illustrated and numerical convergence of the optimization process is demonstrated.

Error Bounds in an Optimization Problem Using the Finite-Element Method

1973 ◽  
Vol 40 (1) ◽  
pp. 204-208
Author(s):  
R. W. McLay ◽  
E. M. Buturla
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Bounds ◽  
Optimization Problem ◽  
Finite Element Solution ◽  
Element Solution ◽  
The Finite Element Method ◽  
The Relationship ◽  
Circular Disks ◽  
Element Method

An optimization problem involving the thermal deflections of two parallel circular disks is examined. Error bounds are developed for both the finite-element solution and the optimization problem. The relationship between the errors is illustrated in a single bound.

NUMERICAL ANALYSIS OF THE FINITE ELEMENT METHOD APPLIED TO THE BOLTZMANN-POISSON SYSTEM

1995 ◽  
Vol 05 (03) ◽  
pp. 351-365 ◽  
Author(s):  
V. SHUTYAEV ◽  
O. TRUFANOV
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Semiconductor Device ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Poisson System ◽  
The Finite Element Method ◽  
Initial Boundary Value ◽  
Element Method

This paper is concerned with the numerical analysis of the mathematical model for a semiconductor device with the use of the Boltzmann equation. A mixed initial-boundary value problem for nonstationary Boltzmann-Poisson system in the case of one spatial variable is considered. A numerical algorithm for solving this problem is constructed and justified. The algorithm is based on an iterative process and the finite element method. A numerical example is presented.

Numerical Analysis of Kinetic Energy Projectile Sabot Structure Influencing the Armour Penetration Depth. Part I - Projectile Basic Option

2021 ◽  
Vol 155 (4) ◽  
pp. 23-48
Author(s):  
Tomasz Błaszczak ◽  
Mariusz Magier
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Kinetic Energy ◽  
Penetration Depth ◽  
Simulation Environment ◽  
The Finite Element Method ◽  
Development Trends ◽  
Terminal Ballistics ◽  
Potential Development

A numerical analysis over influence of kinetic energy projectile sabot structure on the armour depth penetration is presented in the paper. The analysis has identified an influence of sabot different materials into projectile combat performance, and some areas of sabot structure where its shape can be optimised. The finite element method in Solidworks Simulation environment was used in analysis. Due to it the dynamical loads of the sabot at the time of firing could be investi-gated. The influence of sabot different materials and projectile geometry modifications on the strength of penetrator sabot joining was studied. A pattern of dynamical loads for the penetrator sabot joining was simulated and visualised. For selected options of the structure the calculations were performed over the terminal ballistics. It allowed an identification of potential development trends for this brand of ammunition.

NUMERICAL AND PHYSICAL MODELLING OF KAOLIN AS BACKFILL MATERIAL FOR POLYMER CONCRETE RETAINING WALL

2015 ◽  
Vol 76 (2) ◽  
Author(s):  
Ali Arefnia ◽  
Khairul Anuar Kassim ◽  
Houman Sohaei ◽  
Kamarudin Ahmad ◽  
Ahmad Safuan A Rashid
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Retaining Wall ◽  
Laboratory Data ◽  
Physical Modelling ◽  
Horizontal Displacement ◽  
Polymer Concrete ◽  
The Finite Element Method ◽  
Backfill Material

 The failure mechanism of backfill material for retaining wall was studied by performing a numerical analysis using the finite element method. Kaolin is used as backfill material and retaining wall is constructed by Polymer Concrete. The laboratory data of an instrumented cantilever retaining wall are reexamined to confirm an experimental working hypothesis. The obtained laboratory data are the backfill settlement and horizontal displacement of the wall. The observed response demonstrates the backfill settlement and displacement of the retaining wall from the start to completion of loading. In conclusion, numerical modelling results based on computer programming by ABAQUS confirms the experimental results of the physical modelling.  

Finite Element Simulation of RC Beam Strengthened with FRP

2012 ◽  
Vol 446-449 ◽  
pp. 3229-3232
Author(s):  
Chao Jiang Fu
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Finite Element Simulation ◽  
Fiber Reinforced Polymer ◽  
Rc Beam ◽  
The Finite Element Method ◽  
Reinforced Polymer ◽  
Element Simulation

The finite element modeling is established for reinforced concrete(RC) beam reinforced with fiber reinforced polymer (FRP) using the serial/parallel mixing theory. The mixture algorithm of serial/parallel rule is studied based on the finite element method. The results obtained from the finite element simulation are compared with the experimental data. The comparisons are made for load-deflection curves at mid-span. The numerical analysis results agree well with the experimental results. Numerical results indicate that the proposed procedure is validity.

scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

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