Finite Element Method

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A continuous system desribed by differential equations is idealized by a discrete system called the mesh.The discrete system is a collection of elements connected at nodes.A structural problem with an infinite number of degrees of freedom is converted into a problem with a finite number of degrees of freedom, making the probem solvable by a computer.When the nodes are displaced,the elements have an elastic responce within their domain,providing a representation of the elastic properties of the complete system.

 

For continuum mechanics problems, the unknown quantities of the mathematical model are the nodal displacements.The finite element method is based on the folowing matrix equation,which defines the state of equilibrium of forces acting on a structure.

 

Mx..+Bx.+Kx=F

 

Variations of this equation of equilibrium are used to solve different types of structural problems.To solve structural problems,both the displacement method and the minimum potential energy approach are employed.