A machine learning approach to predict the stress results of quadratic tetrahedral elements

Industries are always looking for an effective and efficient way to reduce the computation time of simulation because of the huge expenditure involved. From basics of Finite Element Method (FEM), it is known that, linear order finite elements consume less computation time and are less accurate compared to higher order finite elements say quadratic elements. An approach to get the benefit of less computation cost of linear elements and the good accuracy of quadratic elements can be of a good thought. The methodology to get the accurate results of quadratic elements with the advantage of less simulation run time of linear elements is presented here. Machine Learning (ML) algorithms are found to be effective in making predictions based on some known data set. The present paper discusses a methodology to implement ML model to predict the results equivalent to that of quadratic elements based on the solutions obtained from the linear elements. Here, a ML model is developed using python code, the stress results from Finite Element (FE) model of linear tetrahedral elements is given as the input to it to predict the stress results of quadratic tetrahedral elements. Abaqus is used as the FEM tool to develop the FE models. A python script is used to extract the stresses and the corresponding node numbers. The results showed that the developed ML model is successful in prediction of the accurate stress results for the set of test data. The scatter plots showed that the Z-score method was effective in removing the singularities. The proposed methodology is effective to reduce the computation time for simulation.

Computation of Composite Strengths by Limit Analysis

The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.