3D Strut-and-tie modelling interactive design using peridynamics: Development of a tool for generating strut-and-tie models using peridynamics combined with optimisation for an efficient reinforcement placement
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2022
Författare
Thorsager, Kalle
Udén, Mattias
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The design of discontinuity regions in reinforced concrete structures is usually investigated
in the ultimate limit state with a Strut-and-Tie Model (STM). By using
STM the structure is designed by a lower bound approach according to the theory
of plasticity. This makes the design conservative, assuming that the concrete structure
can undergo sufficient plastic deformation. Therefore, it is good practice to
construct the truss for the STM from the linear stress state in the structure.
A new efficient GPU accelerated method for the particle-based method peridynamics
is proposed to produce the principal stress field in these regions interactively. Voxels
are utilised to discretise the input volume into particles. The use of voxels in the
peridynamics workflow has proved useful in terms that each particle’s neighbour list
is implied and data locality is assured. By implementing the peridynamics solver so
that it utilises the GPU, the run-time of the simulation is drastically decreased on
a personal computer. The boundary conditions are also treated with a new implicit
method which reduces the influence of edge effects close to the boundary.
An initial truss topology is then produced algorithmically by tracing curves in the
principal stress field. Nodes are created at local maximum von Mises points along
these curves and new curves are traced from these nodes. Nodes are also inserted
at relevant intersection points between the traced curves. Based on these principles
an initial truss topology can be created for most structures.
A gradient-based optimisation is applied to the truss topology to get a truss with
minimal reinforcement volume while still fulfilling the checks for the STM in a simplified
manner. The gradient of displacement is used both with regards to the change
of the initial node locations and element areas. The resulting truss and distribution
of the reinforcement will be useful in an early design process but since the exact
placement of the bars is not decided a more detailed analysis will be needed at a
later stage.
The application is useful in terms of understanding the structural behaviour of 3D
structures and estimating the reinforcement volume and placement.
Beskrivning
Ämne/nyckelord
Strut-and-Tie , STM , Particle methods , Peridynamics , Computational design , Topology optimisation , Gradient based optimisation