Design and Optimization of Adhesive Joints for Plate and Disc Components Made of Ultra-High Performance Concrete

When it comes to assembling concrete components, gluing is still a relatively new way of joining. Continuous laminar adhesive joints are especially well-suited to connect thin-walled precast concrete elements in a friction-locked and form-fitted manner. In the subproject of the SPP 1542 program of the DFG easy to use glued joints for plate and disc components were constructed and optimized.

These glued connections are supposed to withstand and transmit load conditions of forces and moments at cut cross sections. The following parameters were investigated:

• the geometry of the glued joints
• the surface properties
• the reinforcements of the concrete elements

Optimization Methods

We primarily used a high performance mineral mortar, also known as reactive-powder concrete adhesive.The optimization of the adhesive joint geometry and the reinforcement close to the joint is based on a mathematically rigorous shape and topology optimization method. In doing so, a level-set function is employed to model the geometry of the joint and the interface of concrete and reinforcement.

Our level set approach was originally developed to compute weight optimized castings. The method makes use of the topological gradient as a measure to quantify the sensitivity of the objective function with respect to the size of local porous inclusions and cracks. On the basis of the investigations were derived:

• decision support for joint designs
• a simplified engineering design model to characterize transmittable forces and moments at cut cross sections

Challenge Tensile Stress

The fundamental problem with gluing is the transmission of tensile stress, since concrete has a relatively small tensile strength. While the tensile strength of plates can be increased by different variants of reinforcements, no reinforcements that bridge the adhesive joint are included here.

Joints with teeth are considered to transfer the applied tensile stresses as shear stresses. For the evaluation and optimization of adhesive bonds of HPC plates precise voltage analysis procedures are necessary.

Rounded Triangular Teeth Optimal

For the shape optimization of glued joints, it is useful to use the XFEM for structure analysis in order to precisely calculate the stresses and distortions in the joint area and to avoid complex new cross-links in the optimization loop.

In the topology and shape optimization, a level set function (see figure) is used to implicitly describe the unknown free or determinable material boundaries, so that a uniform boundary description is provided for the combined topology and shape optimization. The result of the shape optimization for the transmission of tensile stresses is that rounded triangular teeth with a large depth are the most favorable.

The developed methods for structure analysis, topology and shape optimization are usable for any adhesive connections. The materials involved can have any anisotropic stiffness tensors and any structural loads can be considered.