Geometrically nonlinear composite beam structures: design sensitivity analysis

Abstract

The purpose of this paper is to develop a finite element model for optimal design of composite laminated thin-walled beam structures, with geometrically nonlinear behavior, including post-critical behavior. A continuation paper will be presented with design optimization applications of this model. The structural deformation is described by an updated Lagrangean formulation. The structural response is determined by a displacement controlled continuation method. A two-node Hermitean beam element is used. The beams are made from an assembly of flat-layered laminated composite panels. Beam cross-section mass and stiffness property matrices are presented.Design sensitivities are imbedded into the finite element modeling and assembled in order to perform the structural design sensitivity analysis. The adjoint structure method is used. The lamina orientation and the laminate thickness are selected as the design variables. Displacement, failure index, critical load and natural frequency are considered as performance measures. The critical load constraint calculated as the limit point of the nonlinear response is also considered, but a new method is proposed, replacing it by a displacement constraint.

Geometrically nonlinear composite beam structures: optimal design

“…This work complements the paper entitled Geometrically Nonlinear Composite Beam Structures: Design Sensitivity Analysis [1]. In the present paper, the finite element model for analysis and sensitivity analysis developed in that paper is applied to the optimum design of several nonlinear composite laminate beam structures, namely a flat cantilever beam, a dome structure of which the members are beams, and a cantilever arc beam.…”

“…Starting and optimum designs are presented in Table I, where U 11 and V 11 mean node 11 displacements in the x and y directions, respectively, FI 10 means the maximum failure index in element 10, and lower and upper indices of lamina orientation stand respectively for lamina number and laminate number. Note that only one value of FI exists through the thickness of each lamina since it is assumed that the membrane force per unit length is uniform along the laminate thickness [1].…”

“…7). Two equal laminates, 1 Two optimization problems are considered. In the first one the beam is optimized for minimum mass and maximum stiffness, considering lamina orientations and thicknesses of both laminates as design variables.…”

Cross-section optimal design of composite laminated thin-walled beams

“…Design sensitivities of the laminate equivalent elastic constants in Eq. (7) have been presented elsewhere [14].…”

“…Vlasov's theory was extended for the bending and twisting of thin-walled composite beams with open cross-section made from symmetric fiber-reinforced laminates [8,9] and for composite beams with arbitrary geometric and material sectional properties [10,11]. Some papers have also been published dealing with the optimization of composite thin-walled cross-section beams [12][13][14][15].…”