13.189. BEAM189 - 3-D 3-Node Beam

Matrix or Vector Shape Functions Integration Points
Stiffness and Stress Stiffness Matrices; and Thermal and Newton-Raphson Load Vectors Equation 11–19, Equation 11–20, Equation 11–21, Equation 11–22, Equation 11–23, and Equation 11–24

Along the length: 2

Across the section: see BEAM188 - 3-D 2-Node Beam

Consistent Mass Matrix and Pressure, Hydrostatic, and Hydrodynamic Load Vectors Same as stiffness matrix

Along the length: 3 [1]

Across the section: 1

Lumped Mass MatrixEquation 11–19, Equation 11–20, and Equation 11–21

Along the length: 3

Across the section: 1

  1. For partially submerged elements, the hydrostatic/hydrodynamic load vector integration point(s) is/are centered on the wetted portion.

Load Type Distribution
Element Temperature Bilinear across cross-section and linear along length
Nodal Temperature Constant across cross-section, linear along length
Pressure Linear along length. The pressure is assumed to act along the element x-axis.

References: Simo and Vu-Quoc([238]), Ibrahimbegovic([239]).

The theory for this element is identical to that of BEAM188 - 3-D 2-Node Beam, except that it is a 3-node beam element.

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