Monte Carlo Simulation of a Beam Resting on an Elastic Foundation Considering the Two-Dimensional Stochastic Properties of the Elastic Modulus

The analysis of the random behavior of beams on an elastic foundation, considering a two-dimensional random elastic modulus, contributes to bringing the analytical model closer to the physical model of the problem and enhancing the reliability of structural calculations. This paper aims to develop a Monte Carlo simulation (MCs) to represent the two-dimensional random field of elastic modulus combined with the finite element method to analyze the random response of beams resting on an elastic foundation according to the Winkler model. The spectral representation method generates the two-dimensional elastic modulus\u27s Gaussian. This sample function is used to construct the formulation of finite elements. The influence of the random field\u27s standard deviation, the correlation distance along the in-plane axes, and the stiffness of the elastic foundation on the coefficient of variation of displacement are also investigated and analyzed in detail in this article. The two-dimensional randomness of the elastic modulus and the stiffness coefficient of the foundation significantly affect the random response of the beam. The coefficient of variation (COV) of displacement tends to increase when the standard deviation of the stochastic field or the correlation distance along the axes increases. Still, conversely, when the stiffness of the elastic foundation rises, the coefficient of variation decreases. The COV of displacement approaches the standard deviation value of the stochastic field of material properties when the correlation distance along the axes approaches infinity

Monte Carlo Simulation of a Beam Resting on an Elastic Foundation Considering the Two-Dimensional Stochastic Properties of the Elastic Modulus

The analysis of the random behavior of beams on an elastic foundation, considering a two-dimensional random elastic modulus, contributes to bringing the analytical model closer to the physical model of the problem and enhancing the reliability of structural calculations. This paper aims to develop a Monte Carlo simulation (MCs) to represent the two-dimensional random field of elastic modulus combined with the finite element method to analyze the random response of beams resting on an elastic foundation according to the Winkler model. The spectral representation method generates the two-dimensional elastic modulus\u27s Gaussian. This sample function is used to construct the formulation of finite elements. The influence of the random field\u27s standard deviation, the correlation distance along the in-plane axes, and the stiffness of the elastic foundation on the coefficient of variation of displacement are also investigated and analyzed in detail in this article. The two-dimensional randomness of the elastic modulus and the stiffness coefficient of the foundation significantly affect the random response of the beam. The coefficient of variation (COV) of displacement tends to increase when the standard deviation of the stochastic field or the correlation distance along the axes increases. Still, conversely, when the stiffness of the elastic foundation rises, the coefficient of variation decreases. The COV of displacement approaches the standard deviation value of the stochastic field of material properties when the correlation distance along the axes approaches infinity

Stochastic Stability Analysis of Columns with Randomly Elastic Joint Ends and Two-Dimensional Random Material Properties Using Monte Carlo Simulation

This paper develops a Monte Carlo simulation (MCs) to analyze the stochastic stability of a pin-ended column with elastic rotational springs at both ends. The randomness of input factors is considered, including the rotational stiffness of elastic couplings at both ends of the column as random variables following a normal distribution and the elastic modulus of the column as a two-dimensional (2D), stationary, homogeneous Gaussian random field. The spectral representation method is applied to represent the 2D random field and generate realizations of the elastic modulus. The influence of random factors such as the standard deviation of the 2D random field, the standard deviation of normal random variables, and correlation distance in each direction on the coefficient of variation (COV) of the critical load is analyzed in detail in this study. The results indicate a strong correlation between the COV of the critical load and both the standard deviation of the 2D random field and the correlation distance. The COV increases significantly with increasing standard deviation, particularly for larger correlation lengths. However, the influence of the variability of rotational stiffness is relatively minor, especially at larger correlation distances

Stochastic Stability Analysis of Columns with Randomly Elastic Joint Ends and Two-Dimensional Random Material Properties Using Monte Carlo Simulation

This paper develops a Monte Carlo simulation (MCs) to analyze the stochastic stability of a pin-ended column with elastic rotational springs at both ends. The randomness of input factors is considered, including the rotational stiffness of elastic couplings at both ends of the column as random variables following a normal distribution and the elastic modulus of the column as a two-dimensional (2D), stationary, homogeneous Gaussian random field. The spectral representation method is applied to represent the 2D random field and generate realizations of the elastic modulus. The influence of random factors such as the standard deviation of the 2D random field, the standard deviation of normal random variables, and correlation distance in each direction on the coefficient of variation (COV) of the critical load is analyzed in detail in this study. The results indicate a strong correlation between the COV of the critical load and both the standard deviation of the 2D random field and the correlation distance. The COV increases significantly with increasing standard deviation, particularly for larger correlation lengths. However, the influence of the variability of rotational stiffness is relatively minor, especially at larger correlation distances

Exploring Value Co-Destruction Process in Customer Interactions with AI-Powered Mobile Applications

Background: Mobile applications have emerged as important touchpoints for addressing service requests and optimizing human resources. Within the service industry, the integration of artificial intelligence (AI) into these applications has enabled the inference of product demand, provision of personalized service offers, and enhancement of overall firm value. Customers now engage with these apps to stay informed, seek guidance, and make purchases. It is important to recognize that the interactive and human-like qualities of AI can either foster the co-creation of value with customers or potentially lead to the co-destruction of customer value. Although prior research has examined the process of value co-creation, the present study aims to investigate the underlying factors contributing to the value co-destruction process, specifically within AI-powered mobile applications. Method: Our research employs topic modelling and content analysis to examine the value co-destruction process that occurs when customers engage with AI apps. We analyze 7,608 negative reviews obtained from eleven AI apps available on Google Play and App Store AI apps. Results: Our findings reveal six distinct types of value - utilitarian, hedonic, symbolic, social, epistemic, and economic value - that can be co-destroyed during the process. System failure, self-threat and privacy violation are some contributing factors to this value co-destruction process. These values change over time and vary depending on the type of app. Conclusion: Theoretically, our findings extend the concept of value co-destruction in the context of AI apps. We also offer practical recommendations for designing an AI app in a more service-friendly way

Approximation solution for steel concrete beam accounting high-order shear deformation using trigonometric-series

Steel concrete beams have a reasonable structure in terms of using material and high load carrying capacity. This paper deals with an approximate solution based on a trigonometric series for the static of steel concrete beams. The displacement field is based on the higher-order theory using Reddy’s hypothesis. The governing equations are derived from variation principles. An approximate solution based on the representation of displacement fields by trigonometric series is developed to solve the static problem of steel concrete beams. In order to verify the accuracy of the present approximate solution, numerical results are compared with those of exact solutions using classical beam theory. The displacements and nominal stress distributions in the depth direction are obtained with various high of beams. The present approximate approach can accurately predict the displacements and stresses of steel concrete beams

Approximation solution for steel concrete beam accounting high-order shear deformation using trigonometric-series

Steel concrete beams have a reasonable structure in terms of using material and high load carrying capacity. This paper deals with an approximate solution based on a trigonometric series for the static of steel concrete beams. The displacement field is based on the higher-order theory using Reddy’s hypothesis. The governing equations are derived from variation principles. An approximate solution based on the representation of displacement fields by trigonometric series is developed to solve the static problem of steel concrete beams. In order to verify the accuracy of the present approximate solution, numerical results are compared with those of exact solutions using classical beam theory. The displacements and nominal stress distributions in the depth direction are obtained with various high of beams. The present approximate approach can accurately predict the displacements and stresses of steel concrete beams

Exploring Value Co-Destruction Process in Customer Interactions with AI-Powered Mobile Applications

Background: Mobile applications have emerged as important touchpoints for addressing service requests and optimizing human resources. Within the service industry, the integration of artificial intelligence (AI) into these applications has enabled the inference of product demand, provision of personalized service offers, and enhancement of overall firm value. Customers now engage with these apps to stay informed, seek guidance, and make purchases. It is important to recognize that the interactive and human-like qualities of AI can either foster the co-creation of value with customers or potentially lead to the co-destruction of customer value. Although prior research has examined the process of value co-creation, the present study aims to investigate the underlying factors contributing to the value co-destruction process, specifically within AI-powered mobile applications. Method: Our research employs topic modelling and content analysis to examine the value co-destruction process that occurs when customers engage with AI apps. We analyze 7,608 negative reviews obtained from eleven AI apps available on Google Play and App Store AI apps. Results: Our findings reveal six distinct types of value - utilitarian, hedonic, symbolic, social, epistemic, and economic value - that can be co-destroyed during the process. System failure, self-threat and privacy violation are some contributing factors to this value co-destruction process. These values change over time and vary depending on the type of app. Conclusion: Theoretically, our findings extend the concept of value co-destruction in the context of AI apps. We also offer practical recommendations for designing an AI app in a more service-friendly way

Analysis of Beams with a Three-dimensional Random Field of the Modulus of Elasticity Using the Stochastic Finite Element Method

This study proposes a stochastic finite element method (SFEM) for analyzing the static response of beams with material properties modeled as three-dimensional spatial random fields. The method employs weighted integration to discretize spatial variations in Young’s modulus and utilizes a perturbation approach for efficient statistical response computation. Validation is performed using Monte Carlo simulations (MCs) with the spectral representation method to establish a benchmark dataset, showing strong agreement between the two methods, particularly for large correlation distances. The results demonstrate that spatial variability in Young’s modulus significantly affects beam displacement. Shorter correlation lengths reduce displacement variability, while longer correlation lengths lead to greater deflection dispersion. Additionally, an enhancement in the standard deviation of Young's elastic modulus correlates with a higher coefficient of variation (COV) of displacement, confirming structural sensitivity to material randomness. The COV of displacement shows a nearly proportional relationship to the COV of Young’s modulus, which provides key insights into the predictability of stochastic structural behavior. While SFEM is computationally more efficient than MCs, its first-order perturbation formulation limits accuracy in highly nonlinear cases. Future work should explore higher-order stochastic approximations, non-Gaussian random fields, and nonlinear extensions. These findings contribute to advancing stochastic structural analysis by extending SFEM to 3D random fields, providing a foundation for uncertainty quantification in engineering design and highlighting the importance of spatially varying material properties

Teachers’ Assessment of Primary School EFL Learners’ Engagement: Insights from Rural and Urban Classrooms in Vietnam

Learner engagement is increasingly recognized as a crucial factor in language education, especially for young learners. However, research into how teachers perceive and assess learner engagement in intact English as a foreign language (EFL) classrooms remains limited.  This study explored how primary school teachers in urban and rural areas in a Mekong Delta province in Vietnam assessed learner engagement across all four dimensions: behavioral, emotional, cognitive, and social. Employing a quantitative approach, data were collected through a 28-item survey administered to 182 teachers across 63 primary schools. Results indicated that while teachers acknowledged all four dimensions of engagement, they tended to prioritize behavioral and emotional aspects. Geographic location (urban vs. rural) did not significantly influence teachers’ overall assessment, but subtle differences were identified: urban teachers reported slightly higher mean scores for behavioral engagement, while rural teachers exhibited marginally higher scores in cognitive and social dimensions. The findings underscore the importance of a balanced approach to assessing learner engagement. Urban teachers should be guided to view engagement beyond observable participation, while rural teachers should develop a stronger awareness of the role of emotional engagement in sustaining overall learner involvement, particularly in contexts with limited exposure to English such as rural schools