Second-Order Cone Constraints in Structural Analysis

analysis of structures by using the second-order cone constraints;
i.e., (i) stress-unilateral behaviors of cable networks; and
(ii) quasi-static frictional contact problems in three-dimensional
space.

A method is proposed for large deformation analysis of nonlinear
elastic cable networks based on Second-Order Cone Programming (SOCP).
We formulate the constitutive law considering the slackening of cable
into the complementarity conditions over the second-order cones.
Minimization problem of total potential energy is formulated as the
SOCP problem, and the equilibrium configuration is obtained by using
the primal-dual interior-point method.

A Second-Order Cone Linear Complementarity Problem (SOCLCP) is
formulated for the incremental quasi-static problem with unilateral
frictional contact.
The classical Coulomb friction law in three-dimensional space is
considered explicitly without any modification.

The equilibrium configurations are obtained by using a combined
smoothing and regularization method for the second-order cone
complementarity problem.