International Journal of Computational Methods

Smart structures with integrated piezoelectric elements play a pivotal role in mitigating vibrations across diverse applications, by safeguarding against structural damage and performance degradation. This study delves into the active control of vibrations in beams, particularly in fluid-immersed environments where hydrodynamic forces induce complex beam oscillations. The dynamic behavior of geometrically nonlinear, simply supported beams integrated with piezoelectric elements was examined. The position of the piezoelectric patch was optimized through the GA algorithm to minimize the settling time. The optimal location for the piezoelectric patch was determined in the middle of the beam. The investigation encompasses harmonic excitation forces spanning frequencies from 10Hz to 200Hz. Our study evaluates the system’s response under two critical conditions: one with the presence of external hydrodynamic forces and the other without. To achieve effective vibration control, we employ both Proportional-Derivative (PD) and Sliding Mode Controllers (SMC), optimizing their parameters for minimum settling time as an objective function. The results underscore the remarkable superiority of the SMC, reducing settling times by an impressive 50% when compared to the PD controller. Additionally, the SMC demonstrates the ability to significantly reduce control efforts, as evidenced by actuator voltage. In the context of forced vibrations, the SMC maintains its superior performance, especially at lower frequencies. However, at higher frequencies, the emergence of chattering affects the SMC’s performance, although it remains more effective than the PD controller in low-frequency scenarios. This study sheds light on the effectiveness of piezoelectric-based control strategies for smart beams, offering valuable insights into their performance under various vibration conditions. These findings hold significant promise for practical applications where vibration control is critical.

Simplifications in the engineering of artillery firing dynamics modeling introduce model uncertainty, which seriously affects the model’s predictive performance. To this end, a typical variable-section hollow cylindrical cantilever beam structure in artillery firing dynamics is investigated in this paper. The statistical approximation methods quantify parameter and model uncertainty separately, and their respective confidence intervals were calculated and compared. The results show that the traditional parameter uncertainty approach overestimates the parameter uncertainty ranges, and introducing the model uncertainty approach dramatically improves the model prediction performance. Additionally, a projectile-barrel coupled artillery dynamics model considering model uncertainty is established, and its effectiveness is validated through the actual launch experiments. The sensitivity of the dynamic responses to the system matrix, namely model uncertainty, is further analyzed. This paper provides theoretical references for the study of uncertainty in artillery launch dynamics and proposes effective methods to enhance the predictability of computational models for complex structural systems.

The combination of artificial intelligence and finite element method (FEM) is a hot topic in the field of computational mechanics. This study proposes a novel base force element method (BFEM) for finite strain problems based on the complementary energy principle. Using the back-propagation (BP) neural network in the field of artificial intelligence to construct the constitutive relationship of the BFEM for finite strain problems. First, a BFEM model for finite strain problems was derived. Second, using the BP neural network model and learning from test samples, a constitutive relationship for incompressible finite strain problems has been efficiently established. Third, the program has been upgraded using parallel computing and sparse matrices, which greatly improves the computational efficiency of this study. Finally, several finite strain examples were used to verify the correctness of the BFEM based on the BP neural network proposed in this study, as well as the efficiency of the parallel computing method. This study combines BP neural network with a new type of FEM — BFEM, which fills the gap in using complementary energy FEM to calculate the finite strain problem of incompressible hyperelastic materials.

The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same.

To further investigate interaction and competition among various deformation modes in magnesium, a crystal plasticity model incorporating slip, twin, and secondary slip and twin systems is established. This study extends recent molecular dynamics findings to the crystal plasticity framework, introducing a new slip hardening model that incorporates twin boundaries. The proposed unified twin hardening model suitable for both tensile and compressive twins, considers twin stages of nucleation, propagation and growth, thereby simulating twin saturation and coexistence of multiple twin variants. Initially applied to single crystal magnesium, the numerical results agree with experimental findings by Kelley and Hosford, demonstrating twin saturation. We observe that plastic contributions from secondary slip and twin are smaller than those from slip and twins in the parent phase. Furthermore, the plastic contribution from pyramidal I slip is preferred to pyramidal II slip. Next, to study the serious influence of voids on the stress–strain response of ductile solids during manufacturing, the proposed model is then applied to single crystal magnesium containing a void along $c$-axis tension and compression. Both simulations confirm the validity of our crystal plasticity model and its potential to analyze future experimental and molecular dynamic findings.

Numerous novel wave structures, such as lump, lump with one-kink, lump with two-kink soliton, generalized breather, Ma breather, Kuznetsov-Ma breather, Akhmediev breather, manifold periodic, and rogue wave solutions to $(1+1)$-dimensional fifth-order nonlinear Caudrey–Dodd–Gibbon (FNCDG) model via symbolic computation are studied based on the ansatz function scheme. Studying the lump-type solution involves selecting the function as the generic quadratic polynomial function. The lump with one- and two-kink solutions is created by mixing a quadratic function with one or two exponential functions. By adding hyperbolic function with a quadratic function, the rogue wave solutions are manipulated. In addition, the multiwave, $M$-shaped rational solitons and their interactions with kink waves are analytically evaluated. Furthermore, different 3D, 2D, and contour profiles are created in different dimensions by changing the parameter values.

In this paper, we propose an augmented subspace method for solving semilinear parabolic equations based on the Symmetric Interior Penalty Discontinuous Galerkin (SIPDG) method. The main idea of this method is, at each time step, to convert the solution of the semilinear elliptic problem into the solution of the corresponding linear boundary value problem on the same-scale discontinuous finite element space and the solution of the semilinear elliptic problem on a newly defined low-dimensional augmented subspace. The prior error estimates are derived. Numerical experiments are conducted to confirm the theoretical conclusions and the computing efficiency of the proposed method.

Applications for heat exchangers are many and include power plants, air conditioning, chemical and chemical engineering, and other scientific fields. The cost of materials and energy has increased recently, placing pressure on heat exchangers to become even more efficient. In mechanical design, this work proposes a hybrid method for heat transfer optimization and thermal analysis. The proposed hybrid method is the joint execution of both the Wild Horse Optimizer (WHO) and Multi Fidelity Deep Neural Network (MFDNN). It is hence known as the WHO–MFDNN approach. This proposed technique’s goal is to minimize the system’s overall operating costs while optimizing the system’s efficacy. The MFDNN technique is used to forecast the system’s ideal solution, while the proposed WHO approach is employed to minimize the system’s overall operating costs. By then, the proposed approach has been implemented into the MATLAB working platform, and the existing technique is used to compute the execution. In every system now in use, like Artificial Neural Network (ANN), Wild Border Collie Optimization (BCO) and Particle Swarm Optimization (PSO) the proposed approaches produce superior results. It concludes that the proposed method offers superior performance by achieving a cost of $40, converging in just 200 iterations, and requiring only 10 s of computational time, significantly outperforming existing methods with higher costs and longer convergence and computation times.

Integral equations play a vital role in the fields of applied and computational mathematics. This paper introduces a unique subdivision-based collocation technique for solving the initial value problems (IVPs) arising from Volterra integral equations (VIEs). A suitable subdivision scheme is employed to develop the numerical algorithm for solving the VIEs. Several numerical illustrations are tested and compared with the existing methods for assessing the efficiency of the proposed numerical algorithm and error estimation.

The computing of the fundamental period of structures during seismic design is well documented in design codes but is mainly dependent on the height of the structure, which is considered to be the most influential parameter. It is, however, important to consider a phenomenon called the soil–structure interaction (SSI), as this has been found to have a detrimental effect, especially for buildings founded on soft soils. A pilot research project foresaw the use of machine learning (ML) algorithms trained on relatively limited datasets for the development of a more accurate and objective fundamental period formula. Therefore, a dataset that consists of 98,308 fundamental period data points was created through the use of a High-Performance Computer (HPC), which is the largest dataset of its kind. The HPC results were then used to train, test, and validate different ML algorithms. It was found that XGBoost-HYT-CV with hyperparameter tuning performed the best with a correlation of 99.99% and a mean average percentage error (MAPE) of 0.5%. Furthermore, the XGBoost-HYT-CV model outperformed all under-study ML models when using an additional dataset that consisted of out-of-sample building geometries and soil properties, with a resulting MAPE of 9%. Finally, irregular buildings were also used to test the performance of the proposed predictive models.

A hybrid Trefftz finite element method is proposed for solving heat conduction problems in a domain with concave or convex angles. In this method, two temperature fields are independently assumed, one of which is the intra-element field defined inside the element and the other is the frame field defined on the boundary. The corner effects embed in the truncated complete solutions which are used to construct the internal interpolation function for approximating the intra-element field. It is able to accurately analyze the problems with particular corners. The key characteristics lie in the finite element formulation which is evaluated along the element boundary. Compared with the conventional FEM, the corner element does not lose any accuracy by using a small number of elements. Numerical examples demonstrate that the proposed method exhibits low sensitivity to mesh distortion. Compared with ABAQUS, the proposed method also exhibits higher accuracy and a faster convergence rate.

As a classical design method for addressing uncertainty in control systems, robust control is designed with the goal of complete reliability of the control system. Nevertheless, the pursuit of robustness can inadvertently give rise to considerable performance degradation, rendering the resultant closed-loop control system excessively conservative in its design. Reliability-based design methods serve as an effective approach for managing uncertainties, which will achieve a balance between the robustness and performance of the active control system by taking advantage of the characteristic of reliability that allows for a certain level of permissible failure probability. The accurate quantification of uncertainty is the key to achieving reliable control, but common uncertainty quantification methods cannot achieve credible quantification of uncertainty in small samples and update the distribution of new samples. In this paper, a nonprobabilistic Bayesian inference based interval uncertainty quantification method is proposed. This method updates the distribution of interval boundaries and radii by introducing a small number of samples, and obtains interval parameters under a given confidence level. On the basis of uncertainty quantification, the dynamic reliability of the vibration system is derived, and nonprobabilistic reliability is introduced into the design of active controllers through optimization strategies. The reliable control strategy aims to select the optimal controller parameters on a reliable path with a given credibility, in order to solve the problem of overly conservative robust control theory. Two numerical examples were used to verify the feasibility and applicability of this method.

This paper, for the first time, presents a novel meshless method based on the first-order shear deformation theory (FSDT) and moving-least squares (MLS) approximation to carry out static and transient response analysis on arbitrary laminated and sandwich shell structures. The novelty of the method lies in the implementation of MLS in the curvilinear shell formulation, and the derivation of meshless governing equations on the static and transient response of arbitrary laminated and sandwich shells according to the principle of minimum potential energy and Hamilton’s principle, respectively. The concept of a Convected coordinate system is adopted to deal with arbitrary curvilinear surfaces. Both the position and displacement vectors of shells are approximated by MLS, which is conceptually the same procedure as that in the isoparametric finite element method (FEM). The numerical integration of the stiffness matrices is conducted by the simple Gaussian integral in the Convected coordinate system. Because the moving-least squares (MLS) approximation does not satisfy the Kronecker delta condition, the full transformation method is used to modify the meshless governing equations. Numerical examples are calculated to investigate the static and transient response analysis of laminated and sandwich structures with different geometrical shell shapes, including square plates, spherical shells, doubly-curved shells, and cylindrical shells. The numerical tests show that the proposed method is reliable, and robust and produces accurate results compared to the analytical and numerical solutions taken from the previous literature.

The noise emitted is a factor in determining the location for installing wind turbines. It can be a concern for people living near wind farms due to the nuisance and health problems caused by noise emissions. Therefore, noise estimation is one of the most relevant aspects of wind turbine design. Aerodynamic noise can be caused by air motion around the turbine blades. This can create a swooshing or whooshing sound as the blades pass through the air. Aerodynamic noise tends to be more prominent at higher wind speeds when the turbine is operating at full capacity. The trailing edge noise is the main source of wind turbine aerodynamic noise. In this work, semi-analytical solutions for modeling this effect are used. The Ffowcs Williams and Hawkings (FW-H) acoustic analogy is used to predict far-field noise generated by wind turbine blades moving in the air. The equations of the rotor–tower–nacelle structure are obtained by the classical finite element method for a typical onshore wind turbine to predict the blade vibration signal. This new formulation is applied to rotating sources and statistical analysis of broadband trailing edge noise. The novelty of this work is to model the acoustic–structure interaction between the wind flow and the blade structure vibration. In this context, the acoustic far-field pressure emissions are modified by source vibration. In this point, this work compares the acoustic pressure values from rigid and flexible sources. Once the relationship between acoustic emission and wind turbine structural vibration is determined, the potential application of this research is, for example, to provide valuable information about the health and integrity of the blades. Thus, the goal of this work is to predict the aerodynamic noise of a typical large wind turbine taking into account its structural behavior. Therefore, Formulation 1A is used to calculate the far-field noise radiated from the trailing edge of wind turbine blades in a low Mach number flow. The vibration effects are input variables to evaluate the intensity and acoustic pressure values. Some computational aspects are discussed and the numerical model is clarified. The acoustic predictions are validated with analytical results and experimental measurements that are available in the scientific literature. The numerical results of the FW-H acoustic analogy demonstrate that the aerodynamic noise value is predominantly low frequency in the sections closest to the source.