Fuzzy analysis for stability of steel frame with fixity factor modeled as triangular fuzzy number

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme.

A numerical model is presented for both static and dynamic analysis of planar masonry‐infilled steel frames, which are loaded only in their plane. The model can simulate all main nonlinear effects of the frame‐infill‐foundation‐soil system. With this model, bare steel and concrete frame structures, masonry structures, as well as masonry‐infilled steel and concrete frame structures can be analysed. Verification of this model was performed on two experimental tests. In example 1 a masonry‐infilled steel frame under static cyclic load and in example 2 a masonry‐infilled steel frame under dynamic load were analysed. The obtained numerical results agree well with experimental results.

The process parameter selection in any machining process is one of the most challenging criteria for effective machining. Selection of an optimal parametric combination always results in efficient machining. In the current work, a fuzzy TOPSIS method for selection of optimal laser beam micro-marking process parameters, such as current, pulse frequency, and scanning speed, during laser beam marking on gallium nitride is adopted. Response surface methodology (central composite design) is adopted for the experimental design. The mark width, mark depth, and mark intensity are considered as the process responses. The mark width and mark depth are measured with the help of a precision optical microscope. Microscopic images are then treated using image processing software to calculate the mark intensity. A multi-criteria decision-making model is developed considering the effect of process parameters on process response for selection of optimal process parameter in the laser beam micro-marking process. The triangular fuzzy number is used to calculate the weight of each performance criteria, and the fuzzy TOPSIS hybrid approach is used for selection of optimal parametric combination. The results indicate that a small pulse frequency and high current and scanning speed lead to increase in mark intensity.

Integral abutment bridges (IABs) are increasingly adopted in transportation infrastructure due to their durability, reduced maintenance needs, and cost-effectiveness compared to conventional bridges. However, their reliable performance under live loads is strongly influenced by the nonlinear soil–structure interaction (SSI) at the pile–abutment joint, which remains challenging to quantify using conventional analysis methods. This study develops simplified spring-based models to capture the SSI behavior of pile–abutment joints in short-span IABs. Predictive equations for joint rotation, deflection, moment, and shear are formulated using Linear Regression (LR) and Response Surface Methodology (RSM). Unlike prior studies relying solely on FEM or traditional p–y curves, the novelty of this work lies in deriving regression-based spring constants calibrated against FEM analyses, which can be directly implemented in standard structural software. This approach significantly reduces computational demands while maintaining predictive accuracy, enabling efficient assessment of pile contributions and global bridge response. Validation against finite element method (FEM) results confirms the reliability of the simplified models, with RSM outperforming LR in representing nonlinear parameter interactions.

In this master's thesis work, finite element method limitations are investigated in the dynamic analysis of reinforced panels. The panel was modelled using different meshes in order to show that, depending on the element length (or the number of degree of freedom) used in the model, the model does not properly stand for the real structure. In order to assess experimentally the model, an aluminum reinforced panel was built and, through experimental methods, a modal analysis was carried out. The finite element modelling limits were tested and compared to experimental results regarding mid-frequencies. A comparison between finite element and spectral element methods was carried out for computational cost reduction purposes. Due to uncertainties of some model input parameters, a statistical variation was performed using Monte Carlo and Surface Response methods. Results have shown that, at high frequencies the finite element method is not appropriete for dynamic analysis due to high computational costs in high frequency and it is highly sensitive to small variations of the input parameters.

Finite element method (FEM) reveals to be one of the most valuable tools in electric machines design as it accurately takes into account non-linear materials and complex geometry. However, this is by nature an analysis tool, which makes the design procedure very iterative, hence time consuming. Furthermore, the final result is quite uncertain. This main drawback can be eliminated by combining FEM with response surface method (RSM). RSM is a statistical tool to derive experimentally an analytical relationship between a response and some input variables. It is particularly suitable when the underlying phenomenon linking them is not well known or too complex to be modeled mathematically. The relationship is derived by regression from a small number of observations of the response that can be provided by FEM. Genetic algorithm (GA) can then worked directly on this model to optimize the device with a decrease in computational cost. This paper presents the combination of FEM, RSM and GA to optimize the rotor geometry of an interior permanent magnet synchronous motor for fast and accurate design procedure.

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.

This paper deals with the optimum design criteria necessary to minimize the torque ripple of a concentrated winding Synchronous Reluctance Motor (CW-SynRM) using Response Surface Methodology (RSM). The suitability of using RSM with the finite element method (FEM) in practical engineering problems is investigated with computational examples and comparisons between the fitted response and the results obtained from analytical solutions, according to the design variables of stator and rotor in a concentrated winding SynRM (6slot). This research presents efficiency evaluations for a normal synchronous reluctance motor (SynRM) and for a concentrated SynRM (CW-SynRM) using both the coupled transient finite element method (FEM) and Preisach modeling. These evaluations are used to analyze characteristics under the effects of saturation and hysteresis loss. The focus of this research is on an optimum design relative to torque density, ripple characteristics on the basis of stator, rotor shape in a CW-SynRM and efficiency evaluation relative to hysteresis loss, copper loss, etc. on the basis of rated load conditions in a SynRM and CW-SynRM. Computer simulation and experimental results for the efficiency using dynamometer show both the propriety of the proposed design method and the high performance of the CW-SynRM.

Simulation of residual stress in thick thermal barrier coating (TTBC) during thermal shock: A response surface-finite element modeling

This paper presents a procedure a coupling of the finite element method and normal mode technique for obtaining the elastic dynamic response of offshore platforms subjected to arbitrary time and space-dependent forces. The finite element method deals with the complexities of the actual problem by reducing it to an assembly of structural elements, with known elastic and inertial properties, connected together at a discrete number of points on their boundaries. The normal mode technique is then used to reduce the resulting matrix equation of order N to the solution of N single degree-of-freedom equations with certain constraints on the assumed form of damping. An example analysis, utilizing this procedure and an actual offshore platform under the action of two different types of dynamic forces, is presented. These forcing functions are: wave forces as determined through the use of a fifth-order gravity-wave theory and seismic forces as generated by the north-south component of the May 18, 1940, El Centro, California, accelerogram. The platform is assumed to respond according to the assumptions associated with the Bernoulli-Euler beam and bar theory. INTRODUCTION In the field of offshore platform analysis and design, as in many other fields, the tools of analysis are derived through an evolutionary process. As knowledge and ability increase for more accurate prediction of the environmental forces on platforms, the methods of analysis must improve to maintain consistent accuracy. The American Petroleum Institute(l) in its Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms recognizes this evolutionary process and encourages designers of offshore platforms to use "all research advances available to them" The advent of high-capacity, high-speed digital computers has revolutionized the field of structural dynamic analysis. In the past the approach was to reduce the structural model to the simplest form, usually an "equivalent"single-or dual-degree-of-freedom system or "equivalent" beam or bar model for which known closed-form solutions to the dynamic equations were available. While this approach gave valuable insights into the nature of the dynamic response problem, it did not give the detailed elastic response information that is possible today. This paper presents a method which the authors believe is the next step in the evolutionary process of offshore-platform dynamic analysis. It is a combination of the finite element method and the normal mode technique. The finite element method more accurately takes into account the geometry of the system than the so-called "equivalent" methods. Although the finite element method and the normal 'mode technique have been known for a number of years, it is only with advanced computer technology that these approaches have been economically feasible for the analysis of large complex structures. This economic feasibility, the increased accuracy of predictions of dynamic forces on platforms in the operating environment, and the desire of operators to construct offshore platforms in deeper water and use them under more hostile operating conditions, will force designers to use more advanced methods of dynamic analysis.

The finite element method (FEM) is typically used in the process of motor design. However, the FEM requires much computation time. Therefore, decreasing the number of FEM simulations may also decrease the simulation cost. Several optimal design methods overcoming this problem have been recently studied. This paper investigates the optimal design of the magnet pole of a brushless DC motor through reducing simulation cost. The optimization minimizes the magnet volume and limits the average and cogging torques to certain values. In this paper, the response surface methodology and Taguchi's table for decreasing the number of FEM simulations are used to approximate two constraints. The optimization result shows that the presented strategy is satisfactorily performed

During the rolling process of profile ring, the design of the rolling cavity directly affects the forming quality of the final ring. In order to improve the cavity filling rate and reduce the production cycle time, this paper proposes a general evaluation method of the filling difficulty for profile ring rolling cavity by combining the response surface method(RSM) and the finite element method(FEM) with the step-type ring as the research object. Firstly, a universally applicable design method for profile ring rolling cavity is proposed, and based on the description of the rolling cavity, three design variables and a corresponding response objective are defined to achieve multi-objective optimization. Secondly, a finite element model of this step-type ring rolling process is established, and the response model is built and improved by significance analysis and analysis of variance(ANOVA) based on the forming simulation results. Then, the effects of different variables on the optimization objectives are comprehensively investigated by this response model. Finally, the evaluation method of the filling difficulty for profile ring rolling cavity is obtained by combining the contour plot of the response objective.

As the first part of an ongoing integrated project for developing a desktop gantry grinding machine tool, the structural optimization of column part is taken as the focus of the study.The thickness, height, and width of column are the design variables.The objective of optimization is to minimize volume while keeping the deformation of spindle tip smaller than the desired maximum value and the 2nd natural frequency below the given limit.Based on results of static and dynamic analyses obtained from finite element method, the response surface method with factorial design was utilized to create the metamodel for optimization.Two kinds of response surface model with two kinds of factorial design were used for comparison.The gradient search method was applied to the response surface model for optimization.The optimal structure of machine tool made the volume and the second natural frequency both decreasing 13% while the y-displacement of spindle tip were confined to required range.The result shows the successful application of response surface method with carefully chosen factorial design on structural optimization problem.

The present study outlines a sequentially integrated finite-element method (FEM)–response surface method (RSM)–genetic algorithm (GA) framework and implements this to predict the crack parameters, namely, crack location and crack depth ratio. A central composite face centered response surface design of the RSM technique is used to establish the direct relationships between the input parameters (crack location and crack depth ratio) and responses (natural frequencies) to build the response surface function (RSF). Multiple edge cracks are considered, which exist on the top flange of a thin-walled channel section cantilever beam and modeled as line spring elements. In order to obtain RSFs of the first five natural frequencies in terms of process factors such as crack position and crack depth ratio, a number of numerical experiments based on FEM are conducted by using the design-of-experiment approach. An objective function obtained as the square of the difference between RSF and experimentally measured natural frequency has been minimized using GA to find out the optimum crack parameters. Twenty-four steel channel beam specimens have been tested in the laboratory to extract the crack parameters from measured natural frequencies using the proposed approach. The results of the study indicate that the proposed approach performs remarkably, yielding crack parameters with great precision. Copyright © 2015 John Wiley & Sons, Ltd.

Apparent elastic properties of random fiber networks