396,402 research outputs found
Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB
A new topology optimization method called the Proportional Topology
Optimization (PTO) is presented. As a non-gradient method, PTO is simple to
understand, easy to implement, and is also efficient and accurate at the same
time. It is implemented into two MATLAB programs to solve the stress
constrained and minimum compliance problems. Descriptions of the algorithm and
computer programs are provided in detail. The method is applied to solve three
numerical examples for both types of problems. The method shows comparable
efficiency and accuracy with an existing gradient optimality criteria method.
Also, the PTO stress constrained algorithm and minimum compliance algorithm are
compared by feeding output from one algorithm to the other in an alternative
manner, where the former yields lower maximum stress and volume fraction but
higher compliance compared to the latter. Advantages and disadvantages of the
proposed method and future works are discussed. The computer programs are
self-contained and publicly shared in the website www.ptomethod.org.Comment: 18 pages, 8 figures, and 2 appendices (MATLAB codes
Second-order cone programming formulations for a class of problems in structural optimization
This paper provides efficient and easy to
implement formulations for two problems in structural
optimization as second-order cone programming
(SOCP) problems based on the minimum compliance
method and derived using the principle of complementary
energy. In truss optimization both single and
multiple loads (where we optimize the worst-case compliance)
are considered. By using a heuristic which is
based on the SOCP duality we can consider a simple
ground structure and add only the members which
improve the compliance of the structure. It is also
shown that thickness optimization is a problem similar
to truss optimization. Examples are given to illustrate
the method developed in this pape
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