9.17     Free-Field Element

 

            The element is used to input the free-field excitation of a linear soil system to a (nonlinear) soil-structure interacting system.  The method permits the free-field excitation to be specified within the region of computation, arbitrarily close to a zone that includes the (possibly nonlinear) structure and local subgrade and backfill, thus eliminating the need to transmit the seismic excitation through artificial boundaries.  The method and implementation are based on the work reported by Bielak and coworkers (see e.g. Bielak and Christiano [1984]; Cremonini et al [1988]).  The element requires that inside and outside free-field nodes data be defined (see Section 7.5.4).

 

 

References / Bibliography

 

1.            Bielak, J. and Christiano, P., "On the Effective Seismic Input for Non-Linear Soil-Structure Interaction Systems," Earthquake Engineering and Structural Dynamics, Vol. 12 (1984), 107-119.

 

2.            Cremonini, M, Christiano, P. and Bielak, J., “Implementation of Effective Seismic Input for Soil Structure Interaction Systems,” Earthquake Engineering and Structural Dynamics, Vol. 16 (1988), 615-625.

 

9.17.1    Element Control Information

 

Note   Variable Name                    Type        Default      Description

 

           Element_name                      list     [QDC_solid]  Element name

 

           Element_shape                      list           [none]       Element shape (see Fig. 9.2.0)

                 eight_node_brick

                 twenty_node_brick

                 six_node_wedge

                 fifteen_node_wedge

                 four_node_tetra

                 ten_node_tetra

                 four_node_quad

                 eight_node_quad

                 nine_node_quad

                 three_node_tri

                 six_node_tri

 

           Analysis_type                       list          [plane]       Analysis type:

                 plane                                                                  Two-dimensional / plane strain

                 three_dimensional                                              Three-dimensional

 

           Numerical_integration          list            [full]        Numerical integration option:

                 full / reduced                                                     If reduced: one-point Gaussian quadrature

 

           Strain_displacement             list             [*]          Strain-displacement option:

                 standard                                                            Standard formulation

                 bbar_select                                                         Selective-reduced integration

                 bbar_mean                                                          Mean-dilatational formulation

 

           Mass_type                             list        [lumped]     Mass type

                 lumped / consistent                                           If lumped: row-sum technique

 

(1)      Free_field                             list            [on]         Free field option

                 on / off

 

           Number_of_stress_points   integer         [*]          Number of stress points option:

                                                                                            = 1, one stress point

                                                                                            Default:one per integration point

 

 

(cont'd)

 

(cont'd)

 

Note    Variable Name                      Type    Default    Description

 

            Implicit_explicit_type            list         [*]        Implicit/explicit option:

                 implicit                                                              Implicit element

                 explicit                                                              Explicit element

                 implicit_explicit                                               Implicit-explicit element

 

            Body_force_load_time       integer      [0]        Body force load-time function number

 

 

EXAMPLE

            Element_Group  /

                  name = "Group 1"  /

                  element_type = continuum  /

                  element_shape = four_node_quad  /

                  number_of_material_sets = 1  /

                  element_name = QDC_solid  /

                        free_field = on  /

                        strain_displacement = bbar_mean  /

                        number_of_output_sets = 1

 

            Stress_Model  /

                  material_type = linear  /

                  material_name = linear_elastic

                        material_set_number = 1  /

                        youngs_modulus = 1.0E4  /

                        poissons_ratio = 0.25  /

                        solid_mass_density = 2.0  /

                        fluid_mass_density = 1.0  /

                        porosity = 0.30

 

         Body_force      b_x1 = 0.00      b_x2 = 0.00      h = 0.00

 

         Field_output

                  58             0            17

 

         Nodal_connectivity       etc...

 

 

Notes/

(1)               This option requires that inside and outside free_field nodes data be defined (see Section 7.5.4).

 

 

 

9.17.2    Material Data

 

            Material data must be defined for the element group. Consult Chapter 10 for the required input of the individual material models. Note that for this element, it is required that a stress_material_model be prescribed.

 

 

9.17.3    Body Force Data (units: L/T2)

 

BODY_FORCE

 

 

            BODY_FORCE                                   b_x1 = b(1) , ... etc

 

 

 

 

Note    Variable Name     Type     Default      Description

 

(1)        b_x1                      real        [0.0]        Body force component in the x1 direction

 

            b_x2                      real        [0.0]        Body force component in the x2 direction

 

            b_x3                      real        [0.0]        Body force component in the x3 direction

 

 

Notes/

(1) Body force load multipliers are used to define the components of the gravity vector b with respect to the global (x1, x2, x3) coordinate system, e.g., in SI units, b = {0.0, -9.81, 0.0} for the case x2 vertical and oriented positively upward, with g = 9.81 m/s2 and  w = 103 kg/m3.

 

 

9.17.4    Nodal Connectivity Data

 

            Consult Chapter 11 for details. For this element NEN = number of nodes used to define the element (see Fig. 9.2.0.1).  For instance: NEN = 4 in two-dimension (four_node_quad), and NEN = 8 in three-dimension (eight_node_brick).

 

 

 

9.17.5    Output History Requests

 

FIELD_OUTPUT

 

 

            FIELD_OUTPUT

            n,      ng,    ntemp(1),   ntemp(2), etc...

            < etc..., terminate with a blank record >.

 

 

Plots of various element response components may be obtained.  Each component requested is plotted versus time.  Plots of this type are useful in providing quick information concerning the time history behavior of important data.  The total number of components to be plotted must equal Number_output_sets, which is defined on the element group control command (see Section 9.2.0.1).

 

Note             Variable        Default                  Description

 

(1)                     N                 [0]                      Element number  1 and  NUMEL

 

(2)                    NG                [0]                      Generation increment  0

 

(3)              NTEMP(1)          [0]                      Component number  1 and  NCOMP

 

                  NTEMP(2)          [0]                      Component number  1 and  NCOMP

                                                .                                               .

                        etc.                  .                                               .

                                                .                                               .

                  NTEMP(8)          [0]                      Component number  1 and  NCOMP

 

 

Notes/

(1)        Element components history output data must be input for elements at which the time history of one or more components is to be plotted. Terminate with a blank record.

 

(2)        Element components history output data can be generated by employing a two record sequence as follows:

 

                                    Record 1: L, LG, LTEMP(1),..., LTEMP(8)

                                    Record 2: N, NG, NTEMP(1),..., NTEMP(8)

 

The output time history requests of all elements:

 

                                    L+LG, L+2*LG,..., N-MOD(N-L,LG)

 

(i.e., less than N) are set equal to those of element  L.  If LG is zero, no generation takes place between L and N.

 

(2)               Up to three (1D case), seventeen (2D case) and nineteen (3D case) different component numbers may be plotted. The corresponding component numbers and output labels are as follows.

 

 

 

Notes from 9.17.5   (cont'd)

 

Table 9.17.5

 

 

One Dimensional Kinematics (NCOMP=3)

 

        Component Number            Description                                             Output Label

 

                       1                           Normal stress 11                                            S11

                       2                           Strain 11                                                        E11

                       3                           Fluid pressure/Temperature                            PF

 

 

 

 

 

 

Two Dimensional Kinematics (NCOMP=17)

 

        Component Number            Description                                             Output Label

 

                       1                           Normal stress 11                                            S11

                       2                           Normal stress 22                                            S22

                       3                           Normal stress 33                                            S33

                       4                           Shear stress 12                                               S12

                       5                           Principal stress 1                                            PS1

                       6                           Principal stress 2                                            PS2

                       7                           Shear stress                                                  PTAU

                       8                           Stress angle (between PS1 and X1)            SANG

                       9                           Strain 11                                                        E11

                      10                          Strain 22                                                        E22

                      11                          Strain 33                                                        E33

                      12                          Engineering shear strain 12                           G12

                      13                          Principal strain 1                                            PE1

                      14                          Principal strain 2                                            PE2

                      15                          Engineering shear strain                              PGAM

                      16                          Strain angle (between PE1 and X1)           EANG

                      17                          Fluid pressure/Temperature                            PF

 

 

 

Notes from 9.17.5  (cont'd)

 

 

Three Dimensional Kinematics (NCOMP=19)

 

        Component Number              Description                                           Output Label

 

                       1                             Normal stress 11                                          S11

                       2                             Normal stress 22                                          S22

                       3                             Normal stress 33                                          S33

                       4                             Shear stress 12                                             S12

                       5                             Shear stress 23                                             S23

                       6                             Shear stress 31                                             S31

                       7                             Principal stress 1                                          PS1

                       8                             Principal stress 2                                          PS2

                       9                             Principal stress 3                                          PS3

                      10                            Strain 11                                                      E11

                      11                            Strain 22                                                      E22

                      12                            Strain 33                                                      E33

                      13                            Engineering shear strain 12                         G12

                      14                            Engineering shear strain 23                         G23

                      15                            Engineering shear strain 31                         G31

                      16                            Principal strain 1                                          PE1

                      17                            Principal strain 2                                          PE2

                      18                            Principal strain 3                                          PE3

                      19                            Fluid pressure/Temperature                          PF

 

 

 

 

 

 

 

Notes . .

 

 

 

 

Notes . .

 

 

 

 

Notes . .