ИСТИНА

Most of the softwares which are used to make numerical simulation in engineering give mesh-dependent results. So, the purpose of this presentation is to show a method which allows running the simulation with the mesh-independent result. We use the strain gradient theory to solve the problem of a 2D reinforced concrete beam. We consider concrete as a 2D strain gradient continuum. In case of isotropic materials strain energy-density characterized by three material constants, namely two Lamé constants and one length scale parameter [1]. Two embedded reinforcements on both sides of the beam are modeled as a non-material interface. We endowed them with the elastic properties of an Euler-Bernoulli 1D beam. Reinforced cantilever concrete beam bending solutions are obtained using a finite element (FE) approach. The FE simulations showed that solutions with null characteristic lengths are mesh-size dependent. We performed parametric studies to inform the selection of characteristic length parameters associated with the concrete for mesh-size independence. From this parametric study we found the range of reasonable values for characteristic lengths for considered model. In addition, we found the equivalent Young’s modulus of concrete without reinforcements when the characteristic length is zero, and then using this data we determined the equivalent Young’s modulus of the reinforced concrete beam model for various sizes of reinforcing bars for different characteristic lengths L. We use the equivalent Euler-Bernoulli 1D beam to find the equivalent Young’s modulus in cases when the reinforced concrete beam was loaded by a horizontal uniform transverse force (non-uniform bending).