Application of the Generalized Nonlinear Constitutive Law to Hollow-Core Slabs

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Generalized Nonlinear Constitutive Law Applied to Steel Trapezoidal Sheet Plates

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

Prediction of Non-Linear Mechanical Behavior With Deep Neural Network: Application on Low Pressure Turbine Disc

Thanks to the increase of computational capacity and the diversification of computational means, deep learning techniques have shown great successes in learning representations from data in the past decade. Following this trend, efforts have been made in the literature to apply Deep Neural Network (DNN) as surrogate model. Common practice consists in utilizing a single DNN to predict a certain physical property given input design parameters, and the DNN is trained by corresponding simulation results. However, most of the complex high-fidelity simulations involve nonlinear physical laws, e.g. elasto-plasticity, which cannot be explicitly depicted by the applied single DNN model. In the present work, static mechanical simulation with nonlinear constitutive law is addressed with a novel approach in a deep learning framework. We approximate the displacement and the nonlinear constitutive law by two deep neural networks. The first DNN acts as a prior on the unknown displacement field, while the second network aims at describing the nonlinear strain-stress relationship. The dependence of the strainstress relationship on the strain level is taken into consideration by taking the first order derivative with respect to spatial coordinates of the first DNN as an input of the second network. A new loss model combining the error in displacement field prediction and constitutive law description is proposed to train the two DNNs together. We demonstrate the effectiveness of the proposed framework on a low pressure turbine disc design problem.