### Refine

#### Document Type

- Doctoral Thesis (3) (remove)

#### Institute

- Professur Baustatik und Bauteilfestigkeit (3) (remove)

#### Keywords

- ASR (1)
- Alkali-silica reaction (1)
- Beton (1)
- FEM (1)
- Isogeometric analysis (1)
- NURBS (1)
- RHT-splines (1)
- Strukturmechanik (1)
- buildings (1)
- catenary action (1)

Increasing structural robustness is the goal which is of interest for structural engineering community. The partial collapse of RC buildings is subject of this dissertation. Understanding the robustness of RC buildings will guide the development of safer structures against abnormal loading scenarios such as; explosions, earthquakes, fine, and/or long-term accumulation effects leading to deterioration or fatigue. Any of these may result in local immediate structural damage, that can propagate to the rest of the structure causing what is known by the disproportionate collapse.
This work handels collapse propagation through various analytical approaches which simplifies the mechanical description of damaged reinfoced concrete structures due to extreme acidental event.

Alkali-silica reaction causes major problems in concrete structures due to the rapidity of its deformation which leads to the serviceability limit of the structure being reached well before its time. Factors that affect ASR vary greatly, including alkali and silica content, relative humidity, temperature and porosity of the cementitious matrix,all these making it a very complex phenomenon to consider explicitly. With this in mind, the finite element technique was used to build models and generate expansive pressures and damage propagation due to ASR under the influence of thermo-hygrochemoelastic loading. Since ASR initializes in the mesoscopic regions of the concrete,
the accumulative effects of its expansion escalates onto the macroscale level with the development of web cracking on the concrete surface, hence solution of the damage model as well as simulation of the ASR phenomenon at both the macroscale and mesoscale levels have been performed. The macroscale model realizes the effects of ASR expansion as a whole and shows how it develops under the influence of moisture, thermal and mechanical loading. Results of the macroscale modeling are
smeared throughout the structure and are sufficient to show how damage due to ASR expansion orientates. As opposed to the mesoscale model, the heterogeneity of the model shows us how difference in material properties between aggregates and the cementitious matrix facilitates ASR expansion. With both these models, the ASR phenomenon under influence of thermo-chemo-hygro-mechanical loading can be better understood.

This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements.
The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature.
Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical
T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results.