Combined Element Method Research Articles

Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics

We present an approach for solving optimal boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order space-time finite element methods in combination with collocation techniques. Thereby, Cl-regularity in time of the global discrete solution is ensured. The simulation data is used to train solution operators that effectively leverage the higher regularity of the data. The solution operator is represented by Fourier Neural Operators and can be used as the forward solver in the optimal Dirichlet boundary control problem.The proposed algorithm is implemented and tested on high-performance computing platforms, with a focus on efficiency and scalability. The effectiveness of the approach is demonstrated on the problem of generating Terahertz radiation in periodically poled Lithium Niobate. The neural network is used as the solver in the optimal control setting to optimize the parametrization of the optical input pulse and maximize the yield of 0.3THz-frequency radiation.We exploit the periodic layering of the crystal to design the neural networks. The networks are trained to learn the propagation through one period of the layers. The recursive application of the network onto itself yields an approximation to the full problem. Our results indicate that the proposed method can achieve a speedup by a factor of 360 compared to classical methods. A comparison of our results to experimental data shows the potential to revolutionize the way we approach optimization problems in nonlinear optics.

FORMATION OF MODELS AND METHODS FOR ANALYSIS OF STRESS-STRAIN STAND WITH CONTACT INTERACTIONS (REVIEW ARTICLE)

An analysis of the literature and developing models and methods for analyzing the stress-strain system based on the contact interaction between bodies has been conducted. The history of the development of models and methods of analysis of the stress-deformation mill with the protection of contact interaction is considered, which makes it possible to appy the postulates with the drive of what is not necessary: ​​the combination of different types of nonlinearities; transition to a variational formulation of the problem; protection of the surface of contacting bodies; establishment of the method of formalized parametric modeling simultaneously with the combined elements method. Therefore, it is necessary to develop the model, since, in view of the known previous models, they will operate from variable, rather than permanent, physical-mechanical influences on the material of the torsion shafts. It has been concluded that the methods for breaking up the stress-deforming machine, which have been formed, do not support many factors that influence on the elements of armored vehicles, so as not to give an adequate assessment of their value and efficiency durability. The need to move to a variable formulation of the problem and a formalized parametric modeling of processes and stages in the design research of elements of combat armored vehicles simultaneously from the combined element method has been considered. This will make it possible to organize the search for rational design and technological solutions for torsion shafts being part of light armored vehicles with high tactical and technical characteristics. In this case, it is necessary to ensure sufficient adequacy of the model and satisfactory efficiency in numerical investigations. Keywords: light armored vehicle; tactical and technical characteristics; torsion shaft; stress-strain state; strength; durability; elastic-plastic deformation; contact interaction

Stability Analysis of a Multi-Layered Slope in an Open Pit Mine

The design of slopes in open pit mines requires an in-depth understanding of the ground behavior to predict the potential failure mechanism and to better determine the stabilization measures. This study compares the critical slip surface defined by the limit equilibrium method (LEM), the limit analysis (LA), and the finite elements method (FEM) for the stability analysis to better approach the stability on a multi-layered slope. The safety factor, the size, and the location of the critical slip surface obtained from the applied methods are considered in the comparisons. This study highlights some features that affect the slope stability and presents a procedure for addressing the evaluation challenges in a multi-layered formation. Moreover, it presents some aspects of the upper-bound computation on the safety factor of a layered slope subjected to the effects of pore water pressures. Based on the obtained results, the critical slip surface defined by the limit equilibrium method compares well with the slip mechanism suggested by the limit analysis and the finite element approach. In view of the differences in the shape and location of the critical slip surface, as well as the values obtained for the safety factor, it is recommended that an engineer should analyze critical slopes using the finite element method in combination with the limit equilibrium or limit analysis method as a cross reference. The authors propose that in defining the potential failure mass, consideration must be given to the conducted field research and monitoring.

CFD-DEM analysis of the influence of heat storage materials on propane dehydrogenation process

The heat transfer process can significantly affect the propane dehydrogenation (PDH) reaction due to its strongly endothermic nature. This paper describes the influence of heat storage materials (HSM) on the heat transfer and reaction process of PDH, using computational fluid dynamics coupled with discrete element method in combination with reaction kinetics and heat transfer models at the particle scale. During the dehydrogenation, the particle temperature and propane conversion gradually decrease due to the endothermic nature until they become relatively stable. It is found that, initially, HSM particles can provide heat to the reaction through particle–fluid–particle conduction and maintain higher temperature and propane conversion. Gradually, HSM particles can take part in the gas–solid convection and then transfer the heat to the catalyst particles by particle–fluid–particle conduction for the endothermic reaction. Eventually, the heat of reaction and the heat from the hot feed by convection and radiation reach a balance. Furthermore, HSM particles with higher specific heat capacity can provide more heat to the reaction, while the thermal conductivity of HSM particles has insignificant effect on the heat transfer process, since the particle–fluid–particle conduction plays a major role in the heat transfer between particles. This study presents comprehensive understandings of the heat transfer process and the function of HSM particles for endothermic reaction.

Microscale and macroscale strength behaviors of blast furnace slag- cement based materials: Modeling and analysis

Blast furnace slag (BFS) is used extensively as a cement replacement material, improving both the microstructure and the mechanical properties. How to optimize the content of BFS used without losing the mechanical properties of the composite is a very important theoretical problem. Essentially, the strength evolution of BFS-cement based materials is mainly dominated by the hydration reaction of the cementitious material. The formed hydration products bind the dispersed aggregate particles together, so that the material exhibits a certain strength and stiffness on the macroscopic scale. Exploring the microstructural evolution of BFS-cement based materials contributes to the understanding of the failure and instability process under external stress loading, and the optimization of proportion ratios to achieve optimum mechanical properties. Consequently, a better understanding of the microstructure evolution of BFS-cement based material is required. In this study, the microstructure of the BFS-cement based material was modeled using the discrete element method in combination with techniques such as thermogravimetric (TG) analysis and X-ray diffraction (XRD). In addition, mercury intrusion porosimetry and uniaxial compressive strength tests were performed to verify the reliability of the model. Finally, a series of mechanical simulations were carried out using the model. The simulated porosity and compressive strength were compared with the relevant experimental data with an error rate of less than 10%, showing the strong simulation capability of the proposed model. Through representative elementary volume simulation analysis, it is shown that the 30 wt% addition of BFS had a more positive effect on long-term strength, with an increase of approximately 5% compared to that of pure cement sample. The proposed model exhibited that the slag hydration reaction consumes portlandite (CH) and produces more cementitious calcium silicate hydrate (CSH) particles, resulting in the simulated 28d strength starting to be larger than that of pure cement. The established microstructure model of BFS-cement based materials provides a basis for predicting the strength structural.

Microscopic fatigue crack propagation model for polycrystalline alloys

In the present work, using the crystal plasticity finite element method in combination with the extended finite element method, a microscopic polycrystalline fatigue crack propagation (MPFCP) model based on the total cumulative shear strain was developed. MPFCP processes were reproduced well by the MPFCP model. The MPFCP behaviors of micro-single edge notched tensile (M−SENT) and micro-central cracked tension (M-CCT) model specimens under different constraint conditions were analyzed using the new model. Furthermore, the effects of grain orientation on the MPFCP rate and path were discussed. It was found that with the increase of constraints, the number of cycles required for the same MPFCP length increased for both M−SENT and M-CCT model specimens. A crack length of a = 100 μm was the transition length from the microstructurally small crack stage to the physically small crack stage. The diversity of grain orientation distribution had a significant influence on the MPFCP path and rate within each grain.

A New Approach to Identifying an Arbitrary Number of Inclusions, Their Geometry and Location in the Structure Using Topological Optimization

In the present paper, a new approach to identifying an arbitrary number of inclusions, their geometry and their location in 2D and 3D structures using topological optimization was proposed. The new approach was based on the lack of initial information about the geometry of the inclusions and their location in the structure. The numerical solutions were obtained by the finite element method in combination with the method of moving asymptotes. The convergence of the finite element method at the coincidence of functions and their derivatives was analyzed. Results with an error of no more than 0.5%, i.e., almost exact solutions, were obtained. Identification at impact on the plate temperature and heat flux by solving the inverse problem of heat conduction was produced. Topological optimization for identifying an arbitrary number of inclusions, their geometry and their location in 2D problems was investigated.

Actively controllable size-dependent elastic wave band gaps in planar functionally graded micro-lattice

A hybrid planar micro-lattice made of functionally graded materials is proposed where the active and passive constituents are constructed by functionally graded beams with and without partially distributed piezoelectric attachments respectively. The analytical model for predicting complex band structure is presented via the spectral element method in combination with the modified couple stress theory and power law, whose accuracy is validated by the finite element method. By adjusting size dependence, feedback control gain, material gradient and arrangement of piezo-patches, controllable wave propagation and attenuation is achieved, which further advances the implementation of optimizations to obtain ultra-wide low frequency stop bands.

Nonlinear Bending of Sandwich Plates with Graphene Nanoplatelets Reinforced Porous Composite Core under Various Loads and Boundary Conditions

The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction.

Stress strain state of double-layered ferrocement shells under the fire condition

Objective. Development of a method for calculating the bearing capacity of twolayer reinforced cement shells for force and temperature effects in a fire. These structures consist of a fire-retardant layer made of vermiculite concrete, as well as a carrier layer of fine-grained concrete reinforced with mesh.Method. The solution is carried out in a physically nonlinear formulation using the deformation theory of concrete plasticity by G.A. Geniev. In obtaining the resolving equations, the theory of shallow shells by V.Z. Vlasov is used. The physically nonlinear problem reduces to the sequential solution of elastic problems for a structure whose physicomechanical parameters are functions of the x, y, z coordinates. The solution is carried out by the finite element method in combination with the Newton-Raphson method. The dependence of the characteristics of construction materials on temperature is taken into account. The temperature field is assumed to be a function of only one z coordinate, and the finite difference method is used to determine it.Result. the results of numerical simulation of full-scale experiments in a fire chamber for single-layer and two-layer shells are presented. Some deviations are revealed, caused on the one hand by inaccuracies of the experiment and errors of the theory on the other hand.Conclusion. A significant influence of the boundary conditions on the process of deformation of the structure was found. When the support contour was fixed along x and y, a shell bend up was observed, which was consistent with experimental data, and in the case of a freely sliding support contour, the structural points moved exclusively downward. In general, the agreement between the results and experimental data is quite good, which allows us to use the methodology for calculating real structures.

Study of the Mechanical Properties of Wood under Transverse Compression Using Monto Carlo Simulation-Based Stochastic FE Analysis

Wood is an anisotropic material, the mechanical properties of which are strongly influenced by its microstructure. In wood, grain compression strength and modulus are the weakest perpendicular to the grain compared to other grain directions. FE (finite element) models have been developed to investigate the mechanical properties of wood under transverse compression. However, almost all existing models were deterministic. Thus, the variations of geometry of the cellular structure were not considered, and the statistical characteristic of the mechanical property was not involved. This study aimed to develop an approach to investigate the compression property of wood in a statistical sense by considering the irregular geometry of wood cells. First, the mechanical properties of wood under radial perpendicular to grain compression was experimentally investigated, then the statistical characteristic of cell geometry was extracted from test data. Finally, the mechanical property of wood was investigated using the finite element method in combination with the Monte Carlo Simulation (MCS) techniques using randomly generated FE models. By parameter sensitivity analysis, it was found that the occurrence of the yield points was caused by the bending or buckling of the earlywood axial tracheid cell wall in the tangential direction. The MCS-based stochastic FE analysis was revealed as an interesting approach for assessing the micro-mechanical performance of wood and in assisting in understanding the mechanical behavior of wood based on its hierarchical structure.

Dependence of thermogasodynamic parameters of operation of a helicopter gas turbine engine on its operation and dust in the atmosphere

By scanning the blades of the impeller and the guide devices of the full-scale compressor of the helicopter gas turbine engine, a solid-state design model of the compressor with a tunable geometry in the height of the blades was developed. The empirical dependencies of the values of nonlinear wear of the blade of the 1st stage of the compressor on the operating time and the concentration of dust in the air are presented. A block diagram of the procedure for calculating the characteristics and parameters of a helicopter gas turbine compressor is presented. When calculating the flow in the gas–air path of the compressor, the numerical solution of the Navier–Stokes equations averaged by Reynolds, the finite element method in combination with the establishment of patterns of erosive wear of the blades depending on the operating conditions of the engine is used. Mathematical dependencies of the thermogasodynamic parameters of the helicopter gas turbine compressor operation on its operating time and the dustiness of the atmosphere are obtained using modeling. The obtained results can be used in the development of a methodology for automated monitoring of the wear condition of the compressor blades of a helicopter gas turbine engine according to its thermogasodynamic parameters, applied to various climatic operating conditions.

Dynamic Mode Ⅱ fracture behavior of rocks under hydrostatic pressure using the short core in compression (SCC) method

The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitively estimate the dynamic Mode Ⅱ fracture toughness KⅡC of rocks under a triaxial stress state. However, the method for determining the dynamic KⅡC of rocks under a triaxial stress has not been developed yet. With an optimal sample preparation, the short core in compression (SCC) method was designed and verified in this study to measure the dynamic KⅡC of Fangshan marble (FM) subjected to different hydrostatic pressures through a triaxial dynamic testing system. The formula for calculating the dynamic KⅡC of the rock SCC specimen under hydrostatic pressures was obtained by using the finite element method in combination with secondary cracks. The experimental results indicate that the failure mode of the rock SCC specimen under a hydrostatic pressure is the shear fracture and the KⅡC of FM increases as the loading rate. In addition, at a given loading rate the dynamic rock KⅡC is barely affected by hydrostatic pressures. Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.

3D shape optimization of loudspeakers

Improving the performance of loudspeaker units and cabinet designs traditionally relies on a combination of trial and error, sometimes based on a lumped parameter modelling approach. During the last decades, however, large-scale numerical simulations are playing a growing role as a means of improving performance of complex engineering devices such as loudspeakers. However, a numerical model still relies on the experience of the operating engineer to make the appropriate design changes. This can be a difficult task. The use of numerical simulations combined with optimization has a huge potential for further guiding the design process of advanced industrial products where intuition alone is not sufficient. Nevertheless, broadband acoustic simulations are still very time consuming. In this work, we explore the efficiency of a newly proposed semi-analytical adjoint sensitivity approach based on the boundary element method in combination with a lumped parameter model. The sensitivity analysis is used to shape optimize the cabinet of a loudspeaker using free form deformation. The objective of the optimization is to improve frequency responses and directivity patterns.

Stability analysis of wooden arches with account for nonlinear creep

Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete. Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method. Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package. Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods.

On the theory of constitutive equations for composites with different resistance in compression and tension

The paper proposes a new approach to the construction of nonlinear constitutive equations for the description of elastic deformation of fibrous composites with different resistance in compression and tension. The framework of the approach is the generalized rheological method of constructing constitutive equations of the uniaxial stress–strain state. Transition to the tensor equations uses the hypothesis of existence of a special cone of all possible compression states in the space of strains. The cone structure is governed by the reinforcement pattern of a composite. When imposed with strains in the cone, the composite behaves as a linearly elastic medium, while beyond the cone, the composite is nonlinear, with higher stiffness conditioned by tension of high-modulus reinforcement fibers. It is highly critical that the constitutive equations obtained using this approach belong to the theory of hyperelasticity. The elastic potentials of stresses and strains are obtained for these equations, which guarantees implementation of fundamental principles of equilibrium thermodynamics. Application of the developed general theory is exemplified by construction of the constitutive equations for the plane stress state of a thin unidirectional fiber reinforced composite plate and for a multilayer plate with different-direction reinforcement of layers. Using the finite element method in combination with the initial stress method, the stress and strain patterns are analyzed in rectangular one-, two- and three-layer carbon fiber reinforcement polymer plates with a circular cut under the action of external stresses at the boundary.

A Weakly Coupled Fluid Solid Interaction Approach for Hydrostatic Pressure Build-Up in Metal Processing

This paper presents a new modelling approach for liquid lubricant behavior in metal forming operations by focusing on the hydrodynamic pressure build-up in micro pockets. Theoretical and numerical fundamentals of the proposed approach are introduced, and upsetting of an aluminum cylinder with an artificial lubricant pocket is presented as a validation case. The proposed numerical framework splits the fluid-solid interaction model into a computational fluid dynamics and solid mechanics part. While the solid mechanics part employs the Lagrangian finite element flow formulation for plastic deformation, the fluid dynamics part is built upon the set of Navier-Stokes equations applying an Eulerian finite element method in combination with an Arbitrary Langagian Eulerian formalism. The latter enables the displacement based coupling from the solid to the fluid. The fluid-to-solid coupling is pressure based and enabled by the finite element flow formulation’s inherent velocity-pressure characteristics. The weak coupling avoids ill-conditioning of the system matrix and makes it possible to benefit from both Lagrangian and Eulerian meshes.

Trihedral lattice towers geometry optimization

The problem of trihedral lattice towers geometry optimization, the width of which varies linearly with height, has been considered. The variable parameters were the support width at the base and top point, as well as the cross-sectional areas of the lattice and chords. A restriction was introduced on the mass constancy. The objective function was the potential strain energy, the maximum displacement and the first frequency of natural vibrations. In the first and second cases the optimum corresponds to the minimum of the objective function, and in the third - to the maximum. The solution was performed by the finite element method in combination with four nonlinear optimization methods: the interior point method, surrogate optimization method, genetic algorithm and pattern search method. The efficiency of each of the listed optimization methods has been compared by the authors.

Finite element shape optimization of weld orientation in simple plate structure considering different fatigue estimation methods

Dynamically loaded structures are generally in risk of fatigue damage. The fatigue lives of such structures can be improved using traditional methods like producing a better weld or using post-weld treatment. Another method is to improve the overall design of the structure by using the finite element method in combination with shape optimization. In this paper, a framework for finite element shape optimization has been developed, considering the fatigue life of welded joints. Simplicity and the possibility of including different fatigue estimation methods have been in focus for the framework. The framework has been used on a simple plate structure, where the weld orientation has been optimized based on four different fatigue criteria. The results show that the criteria from governing guidelines predict the same optimized weld orientation. However, the critical plane approaches cannot produce optimized weld orientations, when using the nominal stress approach as it does not account for increased stresses from the weld.

The influence of microstructure on crack propagation in cortical bone at the mesoscale

The microstructure of cortical bone is key for the tissue’s high toughness and strength and efficient toughening mechanisms have been identified at the microscale, for example when propagating cracks interact with the osteonal microstructure. Finite element models have been proposed as suitable tools for analyzing the complex link between the local tissue structure and the fracture resistance of cortical bone. However, previous models that could capture realistic crack paths in cortical bone were due to the required computational effort limited to idealized osteon geometries and small (<1 mm2) model domains. The objective of this study was therefore to bridge the gap between experimental and numerical analysis of crack propagation in cortical bone by introducing image-based models at the mesoscale. Tissue orientation maps from high-resolution micro-CT images were used to define the distribution and orientation of weak interfaces in the models. Crack propagation was simulated using the extended finite element method in combination with an interface damage model, previously developed to simulate crack propagation in microstructural osteon models. The results showed that image-based mesoscale models can be used to capture interactions between cracks and microstructure. The simulated crack paths predicted the general trends seen in experiments with more irregular patterns for cracks propagating perpendicular compared to parallel to the osteon orientation. In all, the proposed method enabled an efficient description of the tissue level microstructure, which is a necessity to predict realistic crack paths in cortical bone and is an important step towards simulating crack propagation in bone models in 3D.