E book Particulars :
Language English
Pages 465
Format PDF
Measurement 4.23 MB

 

Finite Element Analysis with Error Estimators by J. E. Akin


 

Finite Element Analysis with Error Estimators An Introduction to the FEM and Adaptive Error Analysis for Engineering College students by J. E. Akin | PDF Free Download.

Contents of Finite Element Analysis PDF E book


Introduction 

  • Finite aspect strategies 
  • Capabilities of FEA 
  • Define of finite aspect procedures 
  • Meeting into the system equations 
  • Error ideas 
  • Workouts 
  • Bibliography

Mathematical preliminaries 

  • Introduction 
  • Linear areas and norms 
  • Sobolev norms
  • Twin issues, self-adjointness 
  • Weighted residuals 
  • Boundary situation phrases
  • Including extra unknowns 
  • Numerical integration 
  • Integration by elements 
  • Finite aspect mannequin downside 
  • Steady nodal flux restoration 
  • A one-dimensional instance error evaluation 
  • Normal boundary situation decisions 
  • Normal matrix partitions 
  • Elliptic boundary worth issues 
  • Preliminary worth issues 
  • Eigen-problems
  • Equal varieties
  • Workouts 
  • Bibliography

Element interpolation and native coordinates 

  • Introduction 
  • Linear interpolation 
  • Quadratic interpolation 
  • Lagrange interpolation 
  • Hermitian interpolation 
  • Hierarchial interpolation 
  • House-time interpolation
  • Nodally precise interpolations
  • Interpolation error
  • Gradient estimates
  • Workouts 
  • Bibliography

One-dimensional integration 

  • Introduction 
  • Native coordinate Jacobian 
  • Actual polynomial integration
  • Numerical integration 
  • Variable Jacobians 
  • Workouts 
  • Bibliography

Error estimates for elliptic issues

  • Introduction 
  • Error estimates 
  • Hierarchical error indicator 
  • Flux balancing error estimates 
  • Element adaptivity 
  • H adaptivity 
  • P adaptivity 
  • HP adaptivity 
  • Workouts 
  • Bibliography

Tremendous-convergent patch restoration 

  • Patch implementation database 
  • SCP nodal flux averaging 
  • Computing the SCP aspect error estimate
  • Hessian matrix
  • Workouts 
  • Bibliography

Variational strategies 

  • Introduction 
  • Structural mechanics 
  • Finite aspect evaluation 
  • Steady elastic bar 
  • Thermal hundreds on a bar
  • Response flux restoration for a component
  • Warmth switch in a rod 
  • Element validation
  • Euler’s equations of variational calculus
  • Workouts 
  • Bibliography

Cylindrical evaluation issues 

  • Introduction 
  • Warmth conduction in a cylinder 
  • Cylindrical stress evaluation 
  • Workouts 
  • Bibliography

Normal interpolation 

  • Introduction 
  • Unit coordinate interpolation 
  • Pure coordinates 
  • Isoparametric and subparametric components 
  • Hierarchical interpolation 
  • Differential geometry
  • Mass properties
  • Interpolation error
  • Element distortion 
  • House-time interpolation
  • Workouts 
  • Bibliography

Integration strategies 

  • Introduction 
  • Unit coordinate integration 
  • Simplex coordinate integration 
  • Numerical integration 
  • Typical supply distribution integrals
  • Minimal, optimum, diminished and chosen integration
  • Workouts 
  • Bibliography

Scalar fields 

  • Introduction 
  • Variational formulation 
  • Element and boundary matrices 
  • Linear triangle aspect 
  • Linear triangle purposes 
  • Bilinear rectangles
  • Normal 2-d components
  • Numerically built-in arrays 
  • Sturdy diagonal gradient SCP take a look at case 
  • Orthtropic conduction 
  • Axisymmetric conduction 
  • Torsion 
  • Introduction to linear flows 
  • Potential movement 
  • Axisymmetric plasma equilibria
  • Slider bearing lubrication 
  • Transient scalar fields 
  • Workouts 
  • Bibliography

Vector fields 

  • Introduction 
  • Displacement based mostly stress evaluation 
  • Planar fashions 
  • Matrices for the fixed pressure triangle 
  • Stress and pressure transformations
  • Axisymmetric strong stress
  • Normal strong stress
  • Anisotropic supplies
  • Round gap in an infinite plate 
  • Dynamics of solids 
  • Workouts 
  • Bibliography

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