Optimisation of CFRP-Strengthened Structures
Research Theme: Computational Design
Many existing reinforced concrete structures built in the 1960s and 1970s are being assessed as having insufficient load capacity. From sustainability and economic perspectives, the repair or strengthening of these structures is often preferable to replacement.
Nevertheless, such an undertaking could cost billions of pounds, and so advanced numerical analysis models are essential in order to develop safe and efficient strengthening strategies.
The analysis of cracked reinforced concrete is notoriously difficult and, because of the nonlinearities in such problems, most existing finite element (FE) simulators are computationally intensive. A further difficulty is the fact that there is minimal (or no) optimisation capability in most FE simulators. Yet to develop efficient strengthening system designs for existing structures, a coupled analytical and optimisation approach is required. Hence, the key challenges are to develop a computationally efficient simulator that can be explicitly used in tandem with appropriate optimisation algorithms to provide a design tool that can identify the parameter sensitivity of various strengthening strategies. The particular application under consideration is the behaviour of concrete beams strengthened with carbon fibre reinforced polymer (CFRP).
- To develop an efficient simulator for reinforced concrete structures (CamEFG)
- To identify and develop appropriate optimisers (e.g. virtual ant algorithms)
- To gain insight into the nonlinear behaviour of CFRP strengthened precracked structures
An efficient meshless/element-free Galerkin simulator (CamEFG) is being developed to simulate the nonlinear behaviour of CFRP strengthened concrete structures. This method is typically 80-100 times faster than a simulation conducted using the conventional FE method.
In addition, appropriate algorithms are being identified and developed for the optimisation of the strengthening system parameters. By combining the meshless simulator and optimiser, a unique approach to the optimisation of the CFRP shear strengthening of precracked concrete structures is being formulated.
CFRP straps or fabric sheets are used for the shear strength enhancement of reinforced concrete structures. For CFRP straps, there are at least five parameters to be adjusted in the design of a CFRP strengthening system. These parameters include the strap locations, spacing, orientation, number and prestress level. Even for a given prestress level (usually 25% or 50%) and a fixed number of CFRP straps of specified orientation, the identification of optimal strap locations and spacings remains a daunting task, because the objective function (ultimate load) cannot be expressed explicitly. In fact, the objective function landscape can only be constructed after the optimisation. So, if the FE simulation time for a candidate strengthening design is about 10 minutes (as it typically is with standard FE methods), the computational cost of solving even a simple two-design-variable optimisation problem can be prohibitive. Unless the simulation and optimisation times for such problems are significantly reduced, optimisation is not a practical proposition.
To address these issues an improved meshfree simulator is being developed concurrently with an improved optimiser. Initial simulations show that the meshless method can capture the effects of the major fractures in the concrete accurately (see Figure 1). This figure shows an unstrengthened beam, a beam with CFRP straps, a beam with fabric sheets and an example of the 3D distribution of strain output. The meshless method has the ability to trace individual cracks, and has two major advantages over conventional FE methods: as there is no FE mesh, only nodes, there is no element degeneracy (i.e. no distorted elements); there is also no need to remesh, which saves a lot of CPU time. The meshless method is also more versatile in dealing with multiple cracks and irregular beam geometries.
Work is also underway testing the effectiveness of novel optimisation procedures using virtual ant algorithms. A sample two-parameter optimisation is shown in Figure 2. In this case a concrete beam with dapped ends is strengthened with additional CFRP reinforcement located at an angle q to the horizontal, a distance w/d from the end of the beam. The aim is to maximise the load capacity. The plot in Figure 2 shows the combination of parameters considered and how the virtual ant algorithm converges on the optimal solution.
It is anticipated that the computational efficiency obtained by combining the meshless method and virtual ant algorithms will improve by a factor of 2000-5000 relative to a conventional analysis repeated for each parameter combination. This would, for the first time, make it practical to seek to optimise the design of CFRP strengthening strategies. Furthermore, although the simulator and optimiser are initially being investigated in the context of CFRP strengthening, the methods are equally applicable to a wide range of other applications.
Support for this project was provided by the EPSRC.
- Highways Agency
- Tony Gee & Partners
- Concrete Society
- Sika Ltd
- YANG, X.S., LEES, J.M., MORLEY, C.T., Application of virtual ant algorithms in the optimization of CFRP shear strengthened precracked structures, Lecture Notes in Computer Sciences, 3991, 834-837 (2006).
- LEES, J.M., MORLEY, C.T., YANG, X.S., HASSAN DIRAR, S., Fibre-reinforced polymer strengthening of precracked concrete structures, Concrete, 39, 36-37 (2005).