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The mechanical efficiency of civil engineering structures is a key factor in the sustainable transformation of the building sector. Topology optimization is a powerful tool for the preliminary draft of mechanically improved structures. The interpretation as a material distribution problem in a predefined design space that is discretized by finite elements is a proven approach to the method; the optimization is performed with respect to a given load profile [1]. The static load of civil engineering structures is typically dominated by their self-weight, which introduces design-dependent loads into the optimization problem. A custom topology optimization routine based on Sequential Quadratic Programming has been developed and applied in the context of sustainable civil engineering design. Previous work has shown that minimizing the elastic strain energy with a constraint on the disposable amount of material yields structures that are characterized by their load transfer mainly by normal forces [2]. Concrete, the most popular construction material in the building sector, exhibits a pronounced tension/compression strength anisotropy. It is known for its high compressive strength and its brittle failure at comparatively low tensile stress [3]. Steel reinforcement increases the tensile strength of the material but is costly compared to fresh concrete and can increase structural self-weight due to its higher mass density. It is therefore desirable that civil engineering structures display load transfer by compressive normal forces.
This study presents topology optimization in civil engineering design with tensile/compressive anisotropic strength, and builds on the findings presented in [4]. A penalization scheme for the stiffness of finite elements subjected primarily to tensile stresses is introduced. The load transfer of each finite element is evaluated in terms of the principal stress with the highest absolute value at its nodes. The approach is tested using benchmark problems considering self-weight. The load transfer of the resulting structures is investigated.
[1] M. P. Bendsøe. “Optimal shape design as a material distribution problem.” Structural Optimization, 1(4):193 – 202, (1989).
[2] Masarczyk, Daniela, et al. "Sustainability in bridge design—investigation of the potential of topology optimization and additive manufacturing on a model scale." PAMM: e202400147, (2024).
[3] B. P. Hughes, and J. E. Ash. “Anisotropy and failure criteria for concrete." Matériaux et Construction 3: 371-374, (1970).
[4] K. Cai. "A simple approach to find optimal topology of a continuum with tension-only or compression-only material." Structural and Multidisciplinary Optimization 43: 827-835, (2011).
