Overview > Framework of VisualFEA > Educational Aids

 

Educational aids

VisualFEA has functions for education in finite element analysis and in structural mechanics. These functions can be used as a tool helpful for teaching and understanding various concepts of finite element analysis and structural mechanics.

> Element stiffness computation

The contents of the element stiffness matrix and other related computation are expanded either in texts of numerical data or in symbolic expressions. The information is organized in hierarchical tree form, and can be expanded selectively. 

  Hierarchical expansion of the information tree
  Matching with the global stiffness matrix
  Toggling numerical expression and symbolic expression
  Real time update of element stiffness information in response to geometry or other assigned data of the model.

> Assembly and solution process

These functions allow the user to examine interactively the procedure of assembling and solving the system equations in a few different forms: full square matrix, upper triangular matrix, band matrix, skyline assembly and frontal solution form. There are functions to display or animate interactively the assembly and solution process of the system equations. 

  Manual display of assembly procedure in the order of element numbering, or in the order specified by the user
  Animation of assembly and solution procedure
  Toggling text and graphic mode
  Matching the part of the model and the part of the matrix
  Displaying the overall status of the system equations
  Matrix partitioning, decomposition, back substitution

> Shape function and interpolation

These educational functions are to visualize graphically the shape functions and their derivatives employed in the finite element modeling. Various characteristics and behavior of interpolation models can be examined interactively. They can be used as a training tool in teaching or learning the concepts and the behavior of element modeling.

  Creating a stiffness model for eigen mode display
  Assigning nodal values to the interpolation model
  Displaying a shape function or interpolated values
  Displaying derivatives of a shape function or interpolated values
  Sampling the numerical value at a specified point or integration points
  Setting rendering modes of shape functions and their derivatives
  Manipulating the view of shape function display

> Eigen mode

The eigenvalues and eigenvectors of the stiffness matrix can be interpreted as a strain energy and corresponding displacement mode, respectively. An eigenvector can be graphically visualized as a displacement mode. The characteristics and the validity of an element can be examined by such a display. The meaning of eigenvalues and eigenvectors can be explored through interactive manipulation of eigen mode display.

 

Creating a stiffness model for eigen mode display
  Animation of eigen modes
  Contouring strain-equivalents of an eigen mode
  Changing integration order and instantly updating eigen modes
  Displaying integration points
  Setting rendering modes of eigenvector
  Manipulating the view of eigen mode display

> Stress recovery and smoothing

Solving the finite element equations gives the values of the primary variables such as displacements in structural analysis or temperatures in heat conduction analysis. Stresses, strains, or heat fluxes are the secondary variables computed from the primary variables. The secondary variables are usually obtained first at integration points and then evaluated at nodal points. This process is called stress recovery and smoothing.  VisualFEA has an educational function to simulated and visualize graphically the stress recovery and smoothing procedure. The computational aspects and characteristics of the procedure can be studied and understood easily using this educational function. 

  Simulating the procedure of stress recovery and smoothing
  Getting details of stress and strain computation
  Comparing the methods of stress smoothing
  Examining intermediate results of stress recovery and smoothing

> Adaptive analysis process

VisualFEA has the capability of adaptive analysis, and has an educational function to visualize this process. Intermediate stages of the adaptive process can be saved and visually reproduced for step by step examination under user's control. This function is intended to help understanding the principles and methods of adaptive solution procedures. 

  Animation of adaptive mesh refinement process
  Comparing computational error and mesh refinement density
  Examining the distribution of energy norm error
  Manipulating the visualization of adaptive process

> Structural behavior

Structural behavior of trusses and frames can be examined by displaying the real time responses to any modification in the structural model. Structural responses such as deformation and member forces are updated immediately after the geometries, element properties, boundary conditions, or load conditions are changed. Thus, the relation between variations in modeling data and their responses can be examined interactively, and this will help understanding the structural behavior.