SMIS: A Stepwise Multiple Integration Solver Using a CAS

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive, since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

A Comparative Study of the Impact of the Stirrer Design in the Stir Casting Route to Produce Metal Matrix Composites

Aluminum matrix composites are widely utilized in many sectors, and their popularity is rising due to their ability to combine high mechanical characteristics with their lightweight. Stir casting is typically achieved in a closed crucible with an invisible flow pattern to produce aluminum alloy matrix composites. Researchers employed a hybrid method to optimize the stir casting parameters. The vast number of parameters and their overlap affects the uniform distribution of reinforcement particles. Investigators on their way to the best technique have gotten promising outcomes in their specific situations, but they still need more work to be able to generalize their findings to optimize the stirrer design to get efficient mixing. Due to an experimental technique alone is insufficient for optimizing stir casting parameters, researchers combined theoretical, experimental, statistical, and numerical simulation approaches to get more precise and reliable findings. The design of the experiment (DOE), particularly Taguchi, and other standard statistics such as ANOVA and regression were discovered to be the most often utilized statistical contributions. Recent attempts to simulate stir casting have begun to match the experimental or analog model data by developed numerical software and analytical analysis. Finally, previous study results and suggestions were collected and compared, arranged, revised, and presented simply about the proper stirrer design, stages, and position in that to make the paper unique.

The effect of the roller profile oncave-in defect in reshaping processby considering nonlinear combine strain hardening

The reshaping process of pipes is an important method in producing non-circular pipes. Desired profile products are produced by passing round pipe through the rotating rollers. Cave-in defect is one of the common defects in the reshaping process. Roller design issues can decrease this kind of defect. In this paper, a method based on the slab method and the incremental plasticity has been presented to the numerical study of a 2D reshaping process. For investigating the Cave-in defect, the contact model has been developed. The concept of element elongation has been introduced to increase the accuracy of the contact model. Based on the presented method, numerical software has been developed to simulate the 2D reshaping process. Elastic-plastic equations for this subject have been driven based on the incremental method, J yielding criterion, and non-linear combined hardening. The effects of the radius of the roller profile on cave-in defects have been investigated by using the presented software (DARF). A set of experiments has been conducted in a forming station to verify the results. Results show that the presented model has higher accuracy than the Abaqus commercial software in predicting the cave-in defect. Based on the results of the model, the local increase of yielding stress directly affects the cave-in defect. Also, a meaningful relationship between the radius of the roller and the amount of the cave-in has been observed.

Calculation of active earth pressure on retaining walls with line surcharge effect and presentation of design diagrams in cohesive – frictional soils

In this study, a formulation and models have been proposed to calculate the active earth pressure on the wall and to determine the angle of failure wedge with line surcharge effect and taking into account the soil cohesion. The proposed method has the advantage of taking into account soil parameters such as cohesion, the angle of friction between the soil and the wall, the surcharge effect in the elasto-plastic environment, and the range that determines the critical surcharge. This paper presents dimensionless diagrams for different soil specifications and surcharges. According to these diagrams, it is easy to determine the distribution of excess pressure caused by surcharge, the distribution of the total active earth pressure on the wall, the angle of the failure wedge as well as the minimum and maximum active coefficient of the pressure with respect to surcharge distance. Furthermore, all soil parameters, surcharge and the results have been addressed. In general, the results indicated that increasing the angle of internal friction of the soil and cohesion would result to a nonlinear reduction in the active earth pressure coefficient, contrary to the line surcharge, which increases the active earth pressure of the soil and ultimately increases the active earth pressure coefficient. In this research, a diagram has been presented that expresses the surface that the active earth pressure coefficient changes with respect to the surcharge distance. The lower limit of each graph expresses the minimum active earth pressure coefficient (kas (min)) at the minimum surcharge distance, whereas the upper limit indicates the maximum active earth pressure coefficient (kas (max)) at the maximum surcharge distance from the wall. Comparison of the results of the proposed method with previous methods, codes and numerical software shows that in general, the proposed method is able to simplify the analysis of walls with surcharge effect in cohesive-frictional soils. In addition to the formulation and diagrams, a computer program in MATLAB software has been written. Using the results of these codes, the pressure on the wall with the linear surcharge effect, angle of failure wedge and pressure distribution on the wall in the cohesive-frictional soils can be calculated for all scenarios.

Influence of Rainfall Intensity on the Stability of Unsaturated Soil Slope: Case Study of R523 Road in Thulamela Municipality, Limpopo Province, South Africa

The purpose of this paper was to analyze the impact of extreme rainfall on the recurrence of slope instability using the Thulamela Municipality roads (R523) as a case study. To this end, the historical rainfall data of the area of study were analyzed between 1988 and 2018. The results show that a significant increase in rainfall is usually experienced in the summer months of December and January. Following this, the factor of safety (FoS) of slopes of silt clay, clay, and clay loam soils were estimated using the SLIDE simulator (Numerical software “Finite Element Method (FEM)”) under sunny to rainy conditions of the area. A complementary model, FLACSlope (Numerical software “Finite Difference Method (FDM)”), was utilized to simulate FoS and pore water pressure in sunny and rainy conditions of the area. Simulation results show that extreme rainfall has the ability to reduce the shear strength and resistance of the soil slope material. This may explain the recurrent landslides noted in the area. Finally, the water pore pressure has been simulated to increase with the increased water table, which generally pushes the soil particles apart and reduces the stress between the particles resulting in soil slope failure. Extreme rainfall alters the phase of the material solid in a manner that may require further research for a better understanding.