A novel approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of unidirectional fiber-reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. The adopted objective function is the same suggested by building codes to design optimal strut-and-tie patterns for reinforced concrete elements. The extension to masonry-like structures is provided by adopting a no-tension model to account for the negligible tensile strength of brickwork. Accordingly, a safe design maximizing the tensile stresses in the reinforcement layer is obtained. The equilibrium of the no-tension body is enforced through the minimization of the elastic strain energy of an equivalent orthotropic medium with constraints on the stress state. This approach to the solution of the elastic problem can be straightforwardly embedded within the topology optimization formulation herein proposed, with the main benefit that the objective function is computed at each iteration of the optimization procedure without resorting to any demanding incremental approach. Assuming perfect bonding between the underlying structure and the overlying reinforcement layer, both elements share the same displacement field. The reinforcing material is assumed to exhibit significant stiffness along one direction, as in the case of unidirectional FRPs. The optimal layout of the reinforcing strips is sought: both the regions to be strengthened and the local orientation of the optimal reinforcement are identified. A suitable set of stress constraints avoids the reinforcement elements to undergo compression. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.

Optimal design of the fiber-reinforcement of no-tension masonry walls

BRUGGI, MATTEO;TALIERCIO, ALBERTO
2017-01-01

Abstract

A novel approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of unidirectional fiber-reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. The adopted objective function is the same suggested by building codes to design optimal strut-and-tie patterns for reinforced concrete elements. The extension to masonry-like structures is provided by adopting a no-tension model to account for the negligible tensile strength of brickwork. Accordingly, a safe design maximizing the tensile stresses in the reinforcement layer is obtained. The equilibrium of the no-tension body is enforced through the minimization of the elastic strain energy of an equivalent orthotropic medium with constraints on the stress state. This approach to the solution of the elastic problem can be straightforwardly embedded within the topology optimization formulation herein proposed, with the main benefit that the objective function is computed at each iteration of the optimization procedure without resorting to any demanding incremental approach. Assuming perfect bonding between the underlying structure and the overlying reinforcement layer, both elements share the same displacement field. The reinforcing material is assumed to exhibit significant stiffness along one direction, as in the case of unidirectional FRPs. The optimal layout of the reinforcing strips is sought: both the regions to be strengthened and the local orientation of the optimal reinforcement are identified. A suitable set of stress constraints avoids the reinforcement elements to undergo compression. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.
2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1027673
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