The Matrix-vector Weak Form — Lesson 1

The development of finite-dimensional weak form is continued. The matrix-vector weak form is discussed. Equations are derived for a general element, then the matrix-vector form is generated using the derived equations.

 

Matrix-vector products are used to eliminate some of the expressions to generate the matrix-vector form. Area and Young’s modulus are assumed to be the constant and the final form for the force and function are written.

 

The establishment of the weak form of matrix-vector will be continued in this video as well. The expression is defined for one element first, then is expanded to sum over all the elements.

 

The expression derived in the last video is now evaluated at the nodes, or at the endpoints of the bi-unit domain. The importance of the Kronecker delta property of the basis function is highlighted for the nodal degrees of freedom, and it is also called the interpolatory property of the space functions. Not all the basis functions have this property. Mapping between degrees of freedom using local and global node numbers is shown or it can be said that the map holds between global and local degrees of freedom.

 

In this video, the task of assembly of the global matrix-vector equations will be carried out. The matrix-vector weak form in terms of global matrices of the vector is written. The element stiffness matrix and element force factor are defined. Finite element assembly is carried out.

 

The finite element weak form assembly for all elements is continued. The matrix assembly for all the elements is continued, and this task is completed in this lesson.