To overcome the non-convexity and non-differentiability of multiple eigenvalues in traditional truss topology optimization models

a unified semidefinite programming (SDP) model was established for truss topology optimization problems with various constraints. Equivalent semidefinite forms were first provided for volume

compliance

fundamental frequency

and global stability constraints. Since the stiffness matrix and the mass matrix of truss are both linear with respect to design variables

problems considering volume

compliance

and fundamental frequency constraints were reformulated as standard dual forms linear SDP. Demonstrated by the global stability constraint and the stress constraint

nonlinear semidefinite constraints and nonlinear scalar constraints were separately approximated by simpler SDP forms at the current design point

which converts the nonlinear model to a solvable approximate SDP model. An algorithm for sequentially solving the approximate problem was then introduced to deal with the nonlinear problem. When the model contains only linear semidefinite constraints

the resultant linear SDP is convex and numerically favorable. When it concerns nonlinear constraints

the sequential approximate scheme enjoys the numerical advantage of linear semidefinite forms and also maintains the ability to handle ordinary nonlinear constraints

which may contribute to a more practical design. Examples show that the proposed SDP model and algorithm could deal with various constraints in truss topology optimization

especially fundamental frequency constraints and global stability constraints with multiple eigenvalues

which verified the effectiveness of the model and the algorithm.