9.11        Multi_Point_Constraints

 

9.11.1     Multi_Point_Constraint

 

               The element is used to impose linear multi nodal point constraint conditions.  A typical constraint equation is written as:

Where the  are the selected nodal point degrees of freedom j at node n.  Constraints may originate from several kinds of physical specifications, such as skewed nodal displacement boundary conditions, interface conditions between regions (solid-solid contact, fluid-solid interactions), etc.  An augmented lagrangian formulation with penalty regularization is used to satisfy the constraints.  Uzawa's algorithm is used to update the lagrange multipliers. A load time function (ltime) can be used to varywith time.

 

MULTI_POINT_CONSTRAINT

 

 

            Element_name = MULTI_POINT_CONSTRAINT

            m,   ltime(m), penalty(m),   c0(m),   ( idof(i,m), c(i,m), i=1,ndof )

                  < connectivity data >

                  < terminate with a blank record >.

 

 

EXAMPLE

            Define_element_group   /

                        name = "mpc"   /

                        element_name = multi_point_constraint   /

                        element_type = interface   /

                        number_of_coeff_1 =  3   /

                        number_of_material_sets = 1

 

            c          m         ltime                penalty   c0                (idof, c1)      (idof, c2)        (idof, c3)

                        1          2                      1 e+3     1.0                  1, 1.0            1, -1.0              2, -1.0

 

            Nodal_connectivity   /

                        input_format = list

                        1          1          1            5        0

                        2          1          6          10        9

 

In this case the element is used to impose the following constraints:

            at nodes 1 and 5:        

            at nodes 6, 9 and 10:  

 

References / Bibliography

 

1.     Arrow, K.J., Hurwicz, L. and Uzawa, H., Studies in Nonlinear Programming, Stanford University Press, Stanford, 1958.

 

9.11.1.1  Element Control Information

 

Note          Variable                   Type                    Default                  Description

 

            Element_name               list                            [*]                     Multi_point_constraint

 

            Element_type                 list                       [interface]              Element_type

 

            Element_shape               list                         [none]                  Element_shape

'

            Number_of_coeff_1      integer           [max [3, 1 + ndof]]     Number of coefficients ci’s

 

    Number_of_material_sets     integer                     [0.0]                    Number_of_material_sets

 

 

 

 

9.11.1.2  Material Properties (Numat sets)

 

Note          Variable           Default                  Description

 

                      M                    [0]                      Geometric/material set number

 

              LTIME(M)              [0]                      Load-time function number

 

            PENALTY(M)        [0.0]                    Penalty coefficient

 

                   C0(M)               [0.0]                    Coefficient

 

               IDOF(i,M)             [0]                      Degree of freedom number j

 

                   C(i,M)               [0.0]                    Coefficient

 

 

 

 

9.11.1.3  Nodal Connectivity Data

 

            Consult Chapter 11 for details; for this element NEN =  number_of_coeff_1

 

 

 

 

9.11.2     Multi_Point_BC

 

               The element is used to impose linear multi nodal point constraint conditions.  A typical constraint equation is written as:

                                                                       

Where the  are the selected nodal point degrees of freedom j at node n.  Constraints may originate from several kinds of physical specifications, such as skewed nodal displacement boundary conditions, interface conditions between regions (solid-solid contact, fluid-solid interactions), etc.  An augmented lagrangian formulation with penalty regularization is used to satisfy the constraints.  Uzawa's algorithm is used to update the lagrange multipliers. A load time function (ltime) is used to apply the constraint as a function of time.

 

MULTI_POINT_BC

 

 

            Element_name = MULTI_POINT_BC

            m,   ltime(m), penalty(m),   c0(m),   ( idof(i,m), c(i,m), i=1,ndof )

                  < connectivity data >

                  < terminate with a blank record >.

 

 

EXAMPLE

            Define_element_group   /

                        name = "mpc"   /

                        element_name = multi_point_BC   /

                        element_type = interface   /

                        number_of_coeff_1 = 3   /

                        number_of_material_sets = 1

 

            c          m         ltime                penalty   c0                (idof, c1)      (idof, c2)        (idof, c3)

                        1          2                      1 e+3     1.0                  1, 1.0            1, -1.0              2, -1.0

 

            Nodal_connectivity   /

                        input_format = list

                        1          1          1            5        0

                        2          1          6          10        9

 

In this case the element is used to impose the following constraints:

            at nodes 1 and 5:        

            at nodes 6, 9 and 10:  

 

 

References / Bibliography

 

1.     Arrow, K.J., Hurwicz, L. and Uzawa, H., Studies in Nonlinear Programming, Stanford University Press, Stanford, 1958.

 

9.11.2.1  Element Control Information

 

Note          Variable                   Type                    Default                  Description

 

            Element_name               list                            [*]                     Multi_point_BC

 

            Element_type                 list                       [interface]              Element_type

 

            Element_shape               list                         [none]                  Element_shape

 

            Number_of_coeff_1      integer           [max [3, 1 + ndof]]     Number of coefficients ci’s

 

    Number_of_material_sets     integer                     [0.0]                    Number_of_material_sets

 

 

 

 

9.11.2.2  Material Properties (Numat sets)

 

Note          Variable           Default                  Description

 

                      M                    [0]                      Geometric/material set number

 

            LTIME(M)                [0]                      Load-time function number

 

            PENALTY(M)        [0.0]                    Penalty coefficient

 

                   C0(M)               [0.0]                    Coefficient

 

               IDOF(i,M)             [0]                      Degree of freedom number j

 

                   C(i,M)               [0.0]                    Coefficient

 

 

 

 

9.11.2.3  Nodal Connectivity Data

 

            Consult Chapter 11 for details; for this element NEN = number_of_coeff_1