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NM3D3

\(N\)-\(M\) Interaction Inelastic Section (Nonlinear Hardening)

Reference

  1. 10.1061/JSENDH.STENG-12176

Syntax

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section NM3D3 (1) (2...14) [(15) (16) (17) (18)...]
# (1) int, unique section tag
# (2) double, EA
# (3) double, strong axis EI
# (4) double, weak axis EI
# (5) double, yielding axial force
# (6) double, yielding strong axis moment
# (7) double, yielding weak axis moment
# (8) double, e
# (9) double, isotropic hardening modulus, H
# (10) double, isotropic hardening saturation, s
# (11) double, isotropic hardening decay, m
# (12) double, kinematic hardening modulus, K_b
# (13) double, kinematic hardening base, K_a
# (14) double, linear density
# (15) double, a_i
# (16) double, b_i
# (17) double, c_i
# (18) double, d_i

In the above command, parameters (15), (16), (17) and (18) form a set and can be appended as many groups as analyst wishes. The surface is assumed to possess the following form,

\[ f=\sum_{i=1}^na_ip^{b_i}m_s^{c_i}m_w^{d_i}-e. \]

For example, the surface \(f=1.15p^2+m_s^2+m_w^4+3.67p^2m_s^2+3p^6m_w^2+4.65m_s^4m_w^2-c\) can be expressed as follows.

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section NM3D3 (1) (2...14) 1.15 2. 0. 0. 1. 0. 2. 0. 3.67 2. 2. 0. 3. 6. 0. 2. 4.65 0. 4. 2.

The only validation implemented is the number of triplets. The command takes \(4n\) parameters and interprets them accordingly. Please make sure the definition is correct.