Optimization of Elastic-Plastic Geometrically Non‐linear Lightweight Structures Under Stiffness and Stability Constraints

Abstract

An actual structural design, especially that of lightweight structures, must evaluate strength, stiffness and stability constraints. A designed structure must satisfy optimality criteria. One faces known difficulties when trying to implement several from above mentioned requirements into optimization problem for further successful numerical realisation. A method to formulate the optimization problem, incorporating all above described criterions, mathematical model and algorithm to solve it numerically, taking into account the geometrically non‐linear structural behaviour are presented for truss type structure. In each optimization cycle the member forces obtained in the previous optimization cycle via elastic‐plastic non‐linear analysis procedure are employed to obtain the new optimal design values. During the optimization procedures, the tension members are assumed to be loaded up to the yield limit, compression members are assumed to be stressed up to their critical limits, the nodal displacements are restricted to limited magnitudes in prescribed directions. Design examples are presented to demonstrate the application of the algorithm.

Optimisation of Geometrically Non‐linear Elastic‐plastic Structures in the State Prior to Plastic Collapse

“…10) to solve the structure, prior to plastic collapse, stress-strain state analysis mathematical model [11,18]:…”

“…It is conditioned by extremely large displacements that have been developed in structures prior to plastic collapse. This phenomenon is met in structures produced from certain materials leading to a violation of regular use requirements [1][2][3][4]. Thus one must keep in mind the abovementioned situations when developing mathematical models of the structural optimisation problems.…”

“…Last three or four decades recognised a rather intensive investigations in development of the structural optimization theory, methods and calculating algorithms; their integration with modern systems of computer modeling and automated design [1][2][3][5][6][7][8][9][10][11][12][13]. Among the most effective methods one can find a methodology of structural optimization joining the mathematical programming theory combined with extreme energy principles and inelastic material response [2,3,5]. It became clear that evaluation of parameters of deformed state of a structure and that of material plastic characteristics serves a more precise reflection of its behaviour at various load stages.…”

“…The task of the present investigations is: • further development of the optimisation problem solution methods, applying extreme dissipated energy principle [3,5] for elastic-plastic geometrically nonlinear structures, evaluating deformed shape influence on structural stiffness; • peculiarities of development of the tangent stiffness matrix considering various structural changes caused by inner forces; • analysis of aspects of numerical modelling of the optimization problems. The proposed techniques are illustrated via solution of sixteen-story single-bay steel frame, subjected by vertical and lateral loads.…”

Optimal shakedown design of metal structures under stiffness and stability constraints

“…Solution of the adapted structure's non-linear optimization problems is complicated as the stress-deformation state of a dissipative system depends on its loading history [9][10][11][12][13][14].…”