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The forces are given by the following equation:

 

                                                 

which can be detailed for a constant thickness finite element with n nodes as:

 

                                     

where Fx and Fy are the body forces about x and y axis such as gravity forces, inertial forces etc. For insance the gravity-loading vector, in plane strain state (h=1) is accumulated element by element from integrals of the type:

 

                                   

where γ denotes the material density of the element and N the shape function matrix. These calculations are performed in the same part of the program that forms the global stiffness matrix. It may be noted that only those freedoms corresponding to vertical movement are incorporated in the integrals. For instance for 3-noded finite elements the gravitational forces are computed as:

 

                                             

assuming that the element is referenced in the global system of coordinates such that the gravitational load acting along y axis.

 

 

 

 

 

 

 

 

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