In finite element modeling, the continuous solid domain is broken down into smaller pieces called elements. Deformation is then computed at selected points called nodes, which are located at the boundaries or specific locations within these elements.
Conditions: Used for discretizing a continuous solid or domain into finite pieces.; Deformation values are associated with selected nodal points.
In finite element modeling, the continuous solid domain is broken down into smaller pieces called elements. Deformation is then computed at selected points called nodes, which are located at the boundaries or specific locations within these elements.
Conditions: Used for discretizing a continuous solid or domain into finite pieces.; Deformation values are associated with selected nodal points.
The video states this as a global law for the finite element approximation: the total perimeter of the polygon formed by all the straight elements must equal the length of the approximated circle. This is the mathematical statement that follows from assembling the individual element equations.
Conditions: Applies to the assembled set of finite elements forming the approximated circle.; The equality is for the approximated polygon, not automatically the original continuous circle.
The video states this as a global law for the finite element approximation: the total perimeter of the polygon formed by all the straight elements must equal the length of the approximated circle. This is the mathematical statement that follows from assembling the individual element equations.
Conditions: Applies to the assembled set of finite elements forming the approximated circle.; The equality is for the approximated polygon, not automatically the original continuous circle.
Discretization error, also called numerical error, is the difference between the circumference of the polygonal approximation (the sum of element lengths) and the true circumference of the original continuous circle. It represents the unavoidable gap introduced when a smooth object is replaced by finite elements.
Conditions: Occurs when a continuous geometry or field is replaced by a finite collection of elements.; In the example, the comparison is between the approximated circle and the original circle.
Discretization error, also called numerical error, is the difference between the circumference of the polygonal approximation (the sum of element lengths) and the true circumference of the original continuous circle. It represents the unavoidable gap introduced when a smooth object is replaced by finite elements.
Conditions: Occurs when a continuous geometry or field is replaced by a finite collection of elements.; In the example, the comparison is between the approximated circle and the original circle.
Element shape functions describe how displacements vary inside a finite element. After the solid is broken into elements and element equations are written, these functions represent the internal variation of displacement within each individual element.
Conditions: Defined within an individual finite element.; Used after discretizing the domain into elements and identifying nodes.
Element shape functions describe how displacements vary inside a finite element. After the solid is broken into elements and element equations are written, these functions represent the internal variation of displacement within each individual element.
Conditions: Defined within an individual finite element.; Used after discretizing the domain into elements and identifying nodes.
A physical law is needed to turn the kinematic description provided by shape functions into a solvable mathematical statement. The law ensures that the mathematical statement is valid both locally within each element and globally over the entire domain.
Conditions: Requires a governing physical principle for the problem class.; The mathematical statement must be valid locally within elements and globally over the domain.
A physical law is needed to turn the kinematic description provided by shape functions into a solvable mathematical statement. The law ensures that the mathematical statement is valid both locally within each element and globally over the entire domain.
Conditions: Requires a governing physical principle for the problem class.; The mathematical statement must be valid locally within elements and globally over the domain.