Computational Modeling of Steel Plate Shear Wall (SPSW) Behavior

Introduction

Steel plate shear wall (SPSW) and reinforced concrete shear wall (RCSW) are two structural members which are mostly used as a lateral resistance system against earthquakes. Furthermore, SPSW and RCSW can be utilized as a resistance system against explosions. However, there is no equation and design method in the handbook or reference book for designing the SPSW and RCSW subjected to blast loads. Also, there is no commercial application to design the structural elements subjected to explosions. These structural members can be simulated by Finite Element Analysis (FEA). Each simulation can take 30 minutes to several hours, and the time and cost of analysis refer to the configuration of the system that is used. Designing an acceptable SPSW and RCSW against explosion requires a minimum of samples in a parametric study. The Taguchi approach is a tool to help the user design the minimum samples for optimization and an acceptable design, although by increasing the number of samples, the accuracy can be increased. Moreover, the number of samples refers to a number of design variables. In order to have a model or equation for optimization, the regression, machine learning, hybrid, and ensemble models should be used. The SPSS, ABAQUS, and MATLAB are used for the models mentioned. This project will utilize three distinct methods, each of which will be the subject of a separate workshop.

What is the steel plate shear wall, and what is its application?

SPSW and RCSW are two structural members that are almost designed and used in the steel frame and reinforced concrete (RC) frame to increase the rigidity of the frame against seismic loads; however, they can be used against explosive loads because the surface absorbs the explosive energy. Therefore, SPSW and RCSW are used to counter seismic load and blast load.

Why a parametric study should be done for this target?

There is no standard, equation, reference book, or design book for the simulation of the steel plate subjected to explosion. Simulation of structural elements subjected to blast loads models is very complex and takes significant time for simulation. There are many design parameters that have an effect on the performance of SPSW and RCSW subjected to blast loads; therefore, many samples should be simulated with various design parameters to specify the effect of the design parameters on the sample behavior.

How many samples should be simulated?

The number of samples refers to the number of design parameters and their levels that can be changed. The levels can be specified according to requirements for design, standards, reality in construction, and any limitation of dimensions. For example, the required sample numbers for a parametric study with four design variables should be at least 91 samples. The design parameters include the dimensions of structural elements, strength of steel and concrete, ratio of steel reinforcement bars, thickness, distance between explosion and structural element, and the weight of TNT. There are several methods, like Taguchi, that can decrease the number of samples that can be used to design an acceptable sample as well as an optimized sample.

Simulation of the sample by finite element method (FEM) using ABAQUS

For the simulation of SPSW and RCSW using FEM, ABAQUS is used in this teaching program. After developing the validated FEA model, the samples, which are specified in the last section, should be simulated and analyzed. The conventional weapons effect program (CONWEP) model is used for the simulation of the explosive load. CONWEP calculates a range of blast effects from different types of high explosives and weapons, including blast loads, fragment penetration depths into concrete and steel, concrete wall breaching, projectile penetration into rock and soil, cratering, and ground shock. Air blast calculations include free-field and reflected blast pressure histories from free-air and surface burst explosions, average peak pressure and impulse from a hemispherical surface burst on a specified reflected wall area, peak pressure from a buried explosion, blast pressure in tunnels, and quasistatic pressure history from a vented internal explosion. the Johnson-Cook model is used for simulation of the steel plate. Von Mises is used in the simulation of the samples. Von Mises stress is a value used to determine if a given material will yield or fracture. It is mostly used for ductile materials, such as metals. The von Mises yield criterion states that if the von Mises stress of a material under load is equal to or greater than the yield limit of the same material under simple tension, then the material will yield. Overall, 125 SPSWs and 255 RCWSs are simulated using ABAQUS.

Simulation of the FEA results using the Artificial Intelligence method

These days, surrogate methods have been developed for presenting the alternative computational method with lower cost and time of calculation. Moreover, using these methods, the optimal design can be specified, and the behavior of the optimal design can be analyzed in a second instead of a complex and long analysis. The surrogate models, which are present in this package, include regression models, Gene Expression Programming, adaptive network-based fuzzy inference system (ANFIS), and hybrid and ensemble models. It is clear that the training dataset and testing datasets should be specified randomly. After training the models using the training datasets, the models should predict the behavior of SPSW and RCSW. All models can be compared based on the time and cost of calculation and accuracy. However, the accuracy of models is compared by the statistical parameters and error terms that include the coefficient of determination, root mean square error (RMSE), normalized square error (NMSE), fractional bias, maximum positive error, maximum negative error, distribution of errors, and mean absolute error.

Method 1: Using SPSS to generate the samples with various parameters

The samples and the variation in design parameters should be logical and based on the standards and reality. To optimize the number of samples for simulation, the Taguchi approach is used by SPSS.

Method 2: Using ABAQUS to validate a FEA model and simulation of all models

ABAQUS is used to validate an FEA model. In order to validate a FEA model, a sensitivity analysis should be conducted. After that, using the validated FEA model, the behavior of samples subjected to explosive loads is simulated.

Method 3: Using ABAQUS to validate a FEA model and simulation of all models

MATLAB is used to develop AI methods, including regression methods, GEP, ANFIS, and ensemble methods. The statistical parameters and error terms are calculated by one of these software.

Workshop 1: Design a parametric study and optimize the number of samples in a parametric study

In thus workshop, first, the effective factors in designing the samples for a parametric study are presented. An appropriate parametric study should consider all effective variables; thus, specifying the effective variables for each parametric study is important. Although by increasing the number of samples, the accuracy of analysis will be increased, the time and cost of analysis will be increased; therefore, in the second part of this workshop, Taguchi as a method for designing a parametric study is explained to optimize the number of samples, although it keeps the accuracy of analysis for a big data.

Workshop 2:  FEA modeling of SPSW and RCSW subjected to explosive loads and validation of FEA model

In this Workshop, the simulation of SPSW and RCWS is explained step by step in ABAQUS software, and after that, four samples that refer to four experimental studies are simulated by ABAQUS. The validation of the FEA model is very important for each FEA model. Therefore, in the end, the validation of the FEA model using mesh sensitivity analysis and comparing the results of FEA with experimental results is presented.

Workshop 3:  Simulation of the behavior of SPSW and RCSW by surrogate models

Using regression models, GEP, Machine Learning (ML), Deep Learning (DL), hybrid, and ensemble models, the behavior of SPSW and RCSW is estimated. For using these approaches, the dataset, which is the collection of design parameters, loading conditions, and the response of SPSW and RCSW to the explosion, is separated randomly into two groups, including training and testing datasets. The training dataset is used to train the surrogate models, and after that, the models are used to predict the response of SPSW and RCSW based on design parameters and explosion conditions. The statistical parameters and error terms are used to compare the model in this Workshop.