With the increasing demand in ocean engineering field for the ultimate limit state(ULS)analysis of thick plates,the solid(3D)element has been more frequently used in the ULS analysis.Compared to 2D element,3D element ...With the increasing demand in ocean engineering field for the ultimate limit state(ULS)analysis of thick plates,the solid(3D)element has been more frequently used in the ULS analysis.Compared to 2D element,3D element can better consider the transverse shearing effect during the analysis which usually occurs on thick plates,due to its reliable reflection of geometrical characteristics and kinematic equations of the structures.Besides,3D element can also facilitate the introduction of influencing factors into the ULS analysis,such as the erosions,cracks and residual stress.This may improve the simulation precision of ULS analysis of thick plate models.Until now,there is a lack of 3D element modelling technique in the ULS analysis of flat/stiffened plates.The present study aims to provide helpful information on 3D elements in the ULS analysis of flat plates under axial compression load.A total of 350 plate scenarios were adopted in the parametric study to consider the effects of 3D element shape(α_(yz)).It is found that the element shape significantly influences the ULS analysis of flat plates,where planar-like 3D element is not recommended.An empirical formula for determining the optimal 3D element shape of the finite element(FE)model is proposed based on the parametric results.A guidance for implementing the 3D elements is then documented,which may help engineers further understand the ultimate strength characteristic of very thick flat plates.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid ...Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.展开更多
Alloy composition design usually contributes to eliminating cracking in Ni-based superalloys during addi-tive manufacturing(AM).However,a detailed understanding of each solid solution element in the crack-ing suscepti...Alloy composition design usually contributes to eliminating cracking in Ni-based superalloys during addi-tive manufacturing(AM).However,a detailed understanding of each solid solution element in the crack-ing susceptibility of Ni-based superalloys during AM is still missing.Thirteen newly designed alloys are considered to investigate the combined effect of solid solution elements on cracking susceptibility.The behaviors of solidification cracking,liquation cracking,and solid-state cracking were analyzed by the microstructural characterization and thermodynamic calculations.The results showed that W and Mo cause the formation of high melting-point carbides at grain boundaries(GBs),which increase solidifica-tion cracking susceptibility.Moreover,W and Mo lead to a slightly higher solidification cracking index(SCI)compared to Co,Cr,and Re.In the successive solidification and remelting process,the borides en-riched in W,Mo,and B around GBs will cause grain boundary segregation and liquation cracking.W and Re extend the freezing range(FR)and exacerbate the segregation of Al and Ti in the inter-dendritic re-gions,contributing to the formation of eutectics.Similarly,complete or partial melting of the eutectic can induce liquation cracking during the thermal cycling in AM.The solid-state cracking susceptibility can be reduced by solid solution elements,especially Re and Co.In summary,compared to Co,Cr,and Re,W and Mo exacerbate the cracking susceptibility.展开更多
In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. ...In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.展开更多
This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support ...This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support to policy-making, on the basis of study on solid waste management status and development trend in China and abroad. Focusing on various treatment and disposal technologies and processes of MSW, this study established a Monte-Carlo mathematical model of cost minimization for MSW handling subjected to environmental constraints. A new method of element stream （such as C, H, O, N, S） analysis in combination with economic stream analysis of MSW was developed. By following the streams of different treatment processes consisting of various techniques from generation, separation, transfer, transport, treatment, recycling and disposal of the wastes, the element constitution as well as its economic distribution in terms of possibility functions was identified. Every technique step was evaluated economically. The Mont-Carlo method was then conducted for model calibration. Sensitivity analysis was also carried out to identify the most sensitive factors. Model calibration indicated that landfill with power generation of landfill gas was economically the optimal technology at the present stage under the condition of more than 58% of C, H, O, N, S going to landfill. Whether or not to generate electricity was the most sensitive factor. If landfilling cost increases, MSW separation treatment was recommended by screening first followed with incinerating partially and composting partially with residue landfilling. The possibility of incineration model selection as the optimal technology was affected by the city scale. For big cities and metropolitans with large MSW generation, possibility for constructing large-scale incineration facilities increases, whereas, for middle and small cities, the effectiveness of incinerating waste decreases.展开更多
An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal str...An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.展开更多
Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming...Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming processes and it is difficult to be simulated accurately with conventional finite element method(CFEM) because it involves solid phase and liquid phase simultaneously.XFEM is becoming more and more popular with the need of solving the discontinuous problem happening in engineering field.The implementation method of XFEM is proposed on Abaqus code by using UEL(user element) with the flowchart.The key is to modify the element stiffness in the proposed method by using UEL on the platform of Abaqus code.In contrast to XFEM used in the simulation of solidification,the geometrical and physical properties of elements were modified at the same time in our method that is beneficial to getting smooth interface transition and precise analysis results.The analysis is simplified significantly with XFEM.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
The effect of various process variables on the law of metal flow for semi-solid rolling 60Si2Mn was studied by finite element method. Semi-solid 60Si2Mn can be described as compressible rigid visco-plastic porous mate...The effect of various process variables on the law of metal flow for semi-solid rolling 60Si2Mn was studied by finite element method. Semi-solid 60Si2Mn can be described as compressible rigid visco-plastic porous material saturated with liquid. In terms of ther-mo-mechanical coupling condition, the distributions of stress, velocity and temperature were studied using software MARC. The simulation results show that the rigid visco-plastic model can accurately describe the semi-solid 60Si2Mn rolling process. The great deformation can achieve completely in view of low flow stress of semi-solid slurry.展开更多
Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. ...Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.展开更多
Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with p...Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with piezoelectricity is derived and a finite element program is developed. Numerical examples are presented to show the effect of nonlinear fracture characteristics on fracture resistance. It is found that an electric field may give a negative driving forceto prevent crack propagation.展开更多
Based on the principle of discrete element method （DEM）, a 2D slot model of a COREX melter gasifier was established to analyze the influence of cohesive zone shape on solid flow, including mass distribution, velocit...Based on the principle of discrete element method （DEM）, a 2D slot model of a COREX melter gasifier was established to analyze the influence of cohesive zone shape on solid flow, including mass distribution, velocity distribution, normal force distribution and porosity distribution at a microscopic level. The results show that the co- hesive zone shape almost does not affect the particle movement in the upper shaft and deadman shape. The particles in the lower central bottom experience large normal force to support the particles above them, while particles around the raceway and in the fast flow zone exhibit weak force network. The porosity distribution was also examined under three kinds of cohesive zones. Like the velocity distribution, the whole packed bed can be divided into four main re- gions. With the increase of cohesive zone position, the low porosity region located in the root of cohesive zone increa- ses. And the porosity distribution becomes asymmetric in the case of biased cohesive zone.展开更多
In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes ...In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.展开更多
基金supported by Brain Pool program funded by the Ministry of Science and ICT through the National Research Foundation of Korea(NRF-2021H1D3A2A02094658)the Basic Science Research Program(NRF-2022R1F1A1065425)support by China government and China scholarship council(CSC NO.202206950035)for this collaborative research.
文摘With the increasing demand in ocean engineering field for the ultimate limit state(ULS)analysis of thick plates,the solid(3D)element has been more frequently used in the ULS analysis.Compared to 2D element,3D element can better consider the transverse shearing effect during the analysis which usually occurs on thick plates,due to its reliable reflection of geometrical characteristics and kinematic equations of the structures.Besides,3D element can also facilitate the introduction of influencing factors into the ULS analysis,such as the erosions,cracks and residual stress.This may improve the simulation precision of ULS analysis of thick plate models.Until now,there is a lack of 3D element modelling technique in the ULS analysis of flat/stiffened plates.The present study aims to provide helpful information on 3D elements in the ULS analysis of flat plates under axial compression load.A total of 350 plate scenarios were adopted in the parametric study to consider the effects of 3D element shape(α_(yz)).It is found that the element shape significantly influences the ULS analysis of flat plates,where planar-like 3D element is not recommended.An empirical formula for determining the optimal 3D element shape of the finite element(FE)model is proposed based on the parametric results.A guidance for implementing the 3D elements is then documented,which may help engineers further understand the ultimate strength characteristic of very thick flat plates.
基金Project supported by the National Basic Research Program of China (973Project) (No.2002CB412709) and the National Natural Science Foundation of China (Nos.50278012,10272027,19832010)
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
文摘Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.
基金supported by the National Science and Technology Major Project,China(Project No.Y2019-Ⅶ-0011-0151)and the Science Center for Gas Turbine Project(Project No.P2022-C-Ⅳ-002-001).
文摘Alloy composition design usually contributes to eliminating cracking in Ni-based superalloys during addi-tive manufacturing(AM).However,a detailed understanding of each solid solution element in the crack-ing susceptibility of Ni-based superalloys during AM is still missing.Thirteen newly designed alloys are considered to investigate the combined effect of solid solution elements on cracking susceptibility.The behaviors of solidification cracking,liquation cracking,and solid-state cracking were analyzed by the microstructural characterization and thermodynamic calculations.The results showed that W and Mo cause the formation of high melting-point carbides at grain boundaries(GBs),which increase solidifica-tion cracking susceptibility.Moreover,W and Mo lead to a slightly higher solidification cracking index(SCI)compared to Co,Cr,and Re.In the successive solidification and remelting process,the borides en-riched in W,Mo,and B around GBs will cause grain boundary segregation and liquation cracking.W and Re extend the freezing range(FR)and exacerbate the segregation of Al and Ti in the inter-dendritic re-gions,contributing to the formation of eutectics.Similarly,complete or partial melting of the eutectic can induce liquation cracking during the thermal cycling in AM.The solid-state cracking susceptibility can be reduced by solid solution elements,especially Re and Co.In summary,compared to Co,Cr,and Re,W and Mo exacerbate the cracking susceptibility.
文摘In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.
基金Project Supported by Tsinghua Research Foundation (No. Jc2003010).
文摘This paper deals with the procedure and methodology which can be used to select the optimal treatment and disposal technology of municipal solid waste （MSW）, and to provide practical and effective technical support to policy-making, on the basis of study on solid waste management status and development trend in China and abroad. Focusing on various treatment and disposal technologies and processes of MSW, this study established a Monte-Carlo mathematical model of cost minimization for MSW handling subjected to environmental constraints. A new method of element stream （such as C, H, O, N, S） analysis in combination with economic stream analysis of MSW was developed. By following the streams of different treatment processes consisting of various techniques from generation, separation, transfer, transport, treatment, recycling and disposal of the wastes, the element constitution as well as its economic distribution in terms of possibility functions was identified. Every technique step was evaluated economically. The Mont-Carlo method was then conducted for model calibration. Sensitivity analysis was also carried out to identify the most sensitive factors. Model calibration indicated that landfill with power generation of landfill gas was economically the optimal technology at the present stage under the condition of more than 58% of C, H, O, N, S going to landfill. Whether or not to generate electricity was the most sensitive factor. If landfilling cost increases, MSW separation treatment was recommended by screening first followed with incinerating partially and composting partially with residue landfilling. The possibility of incineration model selection as the optimal technology was affected by the city scale. For big cities and metropolitans with large MSW generation, possibility for constructing large-scale incineration facilities increases, whereas, for middle and small cities, the effectiveness of incinerating waste decreases.
基金the National Metal and Materials Technology Centerthe Thailand Research Fund+1 种基金the Office of Higher Education Commissionthe Chulalongkorn University for supporting the present research
文摘An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.
基金Project(50972121) supported by the National Nature Science Foundation of ChinaProject(20080004) supported by the Foundation of Key Laboratory for Advanced Materials Processing Technology,Ministry of Education,China
文摘Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming processes and it is difficult to be simulated accurately with conventional finite element method(CFEM) because it involves solid phase and liquid phase simultaneously.XFEM is becoming more and more popular with the need of solving the discontinuous problem happening in engineering field.The implementation method of XFEM is proposed on Abaqus code by using UEL(user element) with the flowchart.The key is to modify the element stiffness in the proposed method by using UEL on the platform of Abaqus code.In contrast to XFEM used in the simulation of solidification,the geometrical and physical properties of elements were modified at the same time in our method that is beneficial to getting smooth interface transition and precise analysis results.The analysis is simplified significantly with XFEM.
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
基金the National Natural Science Foundation of China (No.59995440).
文摘The effect of various process variables on the law of metal flow for semi-solid rolling 60Si2Mn was studied by finite element method. Semi-solid 60Si2Mn can be described as compressible rigid visco-plastic porous material saturated with liquid. In terms of ther-mo-mechanical coupling condition, the distributions of stress, velocity and temperature were studied using software MARC. The simulation results show that the rigid visco-plastic model can accurately describe the semi-solid 60Si2Mn rolling process. The great deformation can achieve completely in view of low flow stress of semi-solid slurry.
基金supported by Department of Energy and Process Engineering,Norwegian University of Science and TechnologyInstitute for Energy Technology and SINTEF through the FACE(Multiphase Flow Assurance Innovation Center) Project
文摘Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.
文摘Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with piezoelectricity is derived and a finite element program is developed. Numerical examples are presented to show the effect of nonlinear fracture characteristics on fracture resistance. It is found that an electric field may give a negative driving forceto prevent crack propagation.
基金Item Sponsored by the Fundamental Research Funds for the Central Universities of China(N090402021)
文摘Based on the principle of discrete element method （DEM）, a 2D slot model of a COREX melter gasifier was established to analyze the influence of cohesive zone shape on solid flow, including mass distribution, velocity distribution, normal force distribution and porosity distribution at a microscopic level. The results show that the co- hesive zone shape almost does not affect the particle movement in the upper shaft and deadman shape. The particles in the lower central bottom experience large normal force to support the particles above them, while particles around the raceway and in the fast flow zone exhibit weak force network. The porosity distribution was also examined under three kinds of cohesive zones. Like the velocity distribution, the whole packed bed can be divided into four main re- gions. With the increase of cohesive zone position, the low porosity region located in the root of cohesive zone increa- ses. And the porosity distribution becomes asymmetric in the case of biased cohesive zone.
文摘In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.
