RKALC Technical Publication
TopoKALC
engineering methodology
Ground-structure topology optimisation and structural load-path exploration for structural form development,
reinforced-concrete D-regions and strut-and-tie model generation within the RKALC engineering workflow.
Engineering basis
Finding the load path before finalising the structural model
TopoKALC addresses an earlier design question than conventional structural analysis: given an allowable region,
applied actions and restraints, what efficient equilibrium load paths are available?
What the publication covers
The technical paper documents the methodology implemented by TopoKALC, including domain discretisation,
generation of a candidate ground structure, geometric admissibility, equilibrium assembly, sparse numerical
solution and post-processing of tension and compression force paths.
It also explains the intended engineering interpretation of the results. TopoKALC is a structural reasoning
and form-exploration tool; its output is not intended to replace engineering judgement, final member sizing,
reinforcement detailing or code verification.
Applications discussed
- Reinforced-concrete D-regions and strut-and-tie model development.
- Transfer walls, discontinuous or walking columns and deep structural regions.
- Walls and domains containing irregular geometry or openings.
- Conceptual steel bracing and structural-form exploration.
- Independent review of engineer-defined load paths and STM idealisations.
- Mesh sensitivity, connectivity controls and interpretation of numerical topology.
RK Software Solutions
TopoKALC
Ground-Structure Topology Optimisation and Structural Load-Path Exploration
Methodology
The TopoKALC ground-structure approach
The implementation uses a discrete axial-member design space rather than a density-based continuum SIMP formulation.
01 · Domain
Engineer-defined geometry
A polygonal design domain is discretised with protected boundary, support and point-load locations retained as structural nodes.
02 · Ground structure
Candidate load paths
Admissible axial members are generated between nodes, subject to connection reach and geometric tests that keep members within the permitted domain.
03 · Equilibrium
Tension and compression variables
The structural problem is assembled from nodal equilibrium equations, with candidate member forces represented through tension and compression variables.
04 · Sparse solution
Efficient numerical solve
A sparse linear-programming procedure is used so that a rich set of possible load paths can be considered without constructing a dense continuum model.
05 · Recovery
Dominant structural mechanism
Signed member forces are recovered, weak or stray branches are rationalised, and the remaining topology is presented as a force-weighted structural network.
06 · Engineering judgement
From topology to design model
The engineer interprets the numerical network, simplifies it into an appropriate structural idealisation and carries that model into detailed design.
RKALC workflow
From structural problem to rationalised STM
The distinction between topology discovery and detailed design is deliberate and central to how TopoKALC is intended to be used.
Design domain, loads and restraints
TopoKALC ground structure
Equilibrium optimisation
Engineer rationalisation
RKALC STM analysis & design
Technical paper
Read the full TopoKALC methodology
The publication includes the engineering basis, mathematical formulation, solver workflow, pseudocode,
current implementation scope, limitations and recommended engineering use.
PDF · Technical publication
TopoKALC — Ground-Structure Topology Optimisation and Structural Load-Path Exploration
First issue: 10 August 2026. The paper describes the implemented RKALC TopoKALC code and distinguishes
the present ground-structure formulation from continuum SIMP and ESO approaches commonly discussed in the literature.
- Engineering basis and relationship to structural load paths.
- Domain discretisation and staggered mesh generation.
- Candidate-member generation and geometric admissibility.
- Stability, connectivity and nodal equilibrium.
- Sparse barrier solution and preconditioned conjugate gradient procedure.
- Recovery and rationalisation of the topology.
- Application to structural concrete, STM and structural form exploration.
- Detailed pseudocode, numerical behaviour and limitations.
TopoKALC Technical Publication
23 pages
Engineering formulation, optimisation mechanism, STM workflow, pseudocode and implementation limits.
Engineering interpretation
TopoKALC is intended to expose mechanically efficient load paths so the engineer can make a better structural idealisation, not to remove the engineer from the design process.
The topology is evidence about force flow. Final strut-and-tie geometry, reinforcement layout, steel framing,
member sizing, nodal-zone verification, detailing and code compliance remain part of the engineer's detailed design responsibility.