LagrangeSP FE


# LagrangeSP_FE

#include <analysis/fe_ele/lagrange/LagrangeSP_FE.h>

class LagrangeSP_FE: public FE_Element ;

FE_Element


LagrangeSP_FE is a subclass of FE_Element used to enforce a single point constraint. It does this by adding to the tangent and the residual: \[\left[ \begin{array}{cc} 0 & \alpha \\ \alpha & 0 \end{array} \right] , \left\{ \begin{array}{c} 0 \\ \alpha(u_s - u_t) \end{array} \right\}\] at the locations corresponding to the constrained degree-of-freedom specified by the SP_Constraint and the lagrange multiplier degree-of-freedom introduced by the LagrangeConstraintHandler for this constraint, where \(U_s\) is the specified value of the constraint and \(U_t\) the current trial displacement at the node corresponding to the constraint.

// Constructor


// Destructor


// Public Methods




To construct a LagrangeSP_FE element to enforce the constraint specified by the SP_Constraint theSP using a value for \(\alpha\) of alpha (which, if none is specified, defaults to \(1.0\)). The FE_Element class constructor is called with the integers \(2\) and \(2\). A Matrix and a Vector object of order \(2\) are created to return the tangent and residual contributions, with the tangent entries (0,1) and (1,0) set at \(\alpha\). A link to the Node in the Domain corresponding to the SP_Constraint is also set. A warning message is printed and program terminates if there is not enough memory or no Node associated with the SP_Constraint exists in the Domain, or DOF_Group is associated with the Node.


Invokes the destructor on the Matrix and Vector objects created in the constructor.


Causes the LagrangeSP_FE to determine the mapping between it’s equation numbers and the degrees-of-freedom. From the Node object link, created in the constructor, the DOF_group corresponding to the Node associated with the constraint is determined. From this DOF_Group object the mapping for the constrained degree of freedom is determined and the myID(0) in the base class is set. The myID(1) is determined from the Lagrange DOF_Group theGroup passed in the constructor. Returns \(0\) if successful. Prints a warning message and returns a negative number if an error occurs: \(-2\) if the Node has no associated DOF_Group, \(-3\) if the constrained DOF specified is invalid for this Node and \(-4\) if the ID in the DOF_Group is too small for the Node.

Returns the tangent Matrix created in the constructor.

Sets the FE_Elements contribution to the residual: \[\left\{ \begin{array}{c} 0 \\ \alpha(u_s - u_t) \end{array} \right\}\] where \(U_s\) is the specified value of the constraint and \(U_t\) the current trial displacement at the node corresponding to constrained degree-of-freedom. Prints a warning message and sets this contribution to \(0\) if the specified constrained degree-of-freedom is invalid. Returns this residual Vector. virtual const Vector &getTangForce(const Vector &disp, double fact = 1.0);
Sets the FE_Elements contribution to the residual: \[\left\{ \begin{array}{c} 0 \\ \alpha(u_s - u_t) \end{array} \right\}\] where \(U_s\) is the specified value of the constraint and \(U_t\) the current trial displacement in disp corresponding to constrained degree-of-freedom. Prints a warning message and sets this contribution to \(0\) if the specified constrained degree-of-freedom is invalid.

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