Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols ...This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata （DFA） and nondeterministic finite automata （NFA）.展开更多
This paper presents the effects of surface finish and treatment on the high cycle fatigue behaviour of vibrating cylinder block of a new two-stroke free piston engine at complex variable amplitude loading conditions u...This paper presents the effects of surface finish and treatment on the high cycle fatigue behaviour of vibrating cylinder block of a new two-stroke free piston engine at complex variable amplitude loading conditions using frequency response approach. Finite element modelling and frequency response analysis was conducted using finite element analysis software Package MSC.PATRAN/MSC.NASTRAN and fatigue life prediction was carded out using MSC.FATIGUE software. Based on the finite element results, different frequency response approach was applied to predict the cylinder block fatigue life. Results for different load histories and material combinations are also discussed. Results indicated great effects for all surface finish and treatment. It is concluded that polished and cast surface finish conditions give the highest and lowest cylinder block lives, respectively; and that Nitrided treatment leads to longest cylinder block life. The results were used to draw contour plots of fatigue life and damage in the worst or most damaging case.展开更多
The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using t...The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using the 20-node solid elements is generated. A linear elastic finite element analysis was performed, hotspot stresses in a web-frame joint were analyzed and fatigue damage was quantified employing the S-N approach. The statistical descriptors of the fatigue life of a non-correlated web-frame joint containing several critical hotspots were estimated. The fatigue reliability of a web-frame joint wasmodeled as a series system of correlated components using the Ditlevsen bounds. The fatigue reliability of the entire welded structure with multiple web-frame joints, modeled as a parallel system of non-correlated web-frame joints was also calculated.展开更多
Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadr...Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.展开更多
A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that th...A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that the new insights may be taken into account as decision points to outperform the available materials. It is to note that the traditional control approaches may generally be upgraded, as long as a number of modifications are made with respect to state-of-the-art, in order to propose high-precision outcomes. Regarding the investigated issues, the robust sliding mode finite-time control approach is first designed to handle three-axis angular rates in the inner control loop, which consists of the pulse width pulse frequency modulations in line with the control allocation scheme and the system dynamics. The main subject to employ these modulations that is realizing in association with the control allocation scheme is to be able to handle a class of overactuated systems, in particular. The proportional derivative based linear quadratic regulator approach is then designed to handle three-axis rotational angles in the outer control loop, which consists of the system kinematics that is correspondingly concentrated to deal with the quaternion based model. The utilization of the linear and its nonlinear terms, simultaneously, are taken into real consideration as the research motivation, while the performance results are of the significance as the improved version in comparison with the recent investigated outcomes. Subsequently, there is a stability analysis to verify and guarantee the closed loop system performance in coping with the whole of nominal referenced commands. At the end, the effectiveness of the approach considered here is highlighted in line with a number of potential recent benchmarks.展开更多
Residual stress plays a vital role in the structural strength and stability. The determination of residual stress at single-point has become mature at present. However, the method to determine residual stress distribu...Residual stress plays a vital role in the structural strength and stability. The determination of residual stress at single-point has become mature at present. However, the method to determine residual stress distribution is still in shortage. For this problem, a finite element approach combined with slot milling method was developed in this study. In the method, firstly a slot is milled on the specimen surface to release the residual stress and then the released displacement field is measured by optical method, such as digital image correlation （DIC）, finally the finite element approach is used to determine the residual stress distribution along the slot. In order to verify the feasibility of the method, it was applied to study the residual stress introduced by shot peening, mainly about the stress distribution along the direction vertical to the shot peened surface. Since the influence depth of shot peening was too small, we utilized focused ion beam （FIB） to determine the microscale residual stress distribution. The result measured by X-ray diffraction （XRD） demonstrated that the method was feasible to determine the residual stress distribution.展开更多
In this paper,a novel 2-DOF rotational pointing mechanism(RPM)is designed inspired by the guidelines of the graphical approach.The mechanism integrates with a fast steering mirror(FSM)for compensating pointing errors ...In this paper,a novel 2-DOF rotational pointing mechanism(RPM)is designed inspired by the guidelines of the graphical approach.The mechanism integrates with a fast steering mirror(FSM)for compensating pointing errors of a laser beam.The design intends to achieve an angular travel of±10 mrad and steers a 25 mm mirror aperture.A planar flexure with beam flexures accompanied in parallel with an axial flexure build-up mechanism configuration.Compliant mechanismbased RPM ensures high precision and compactness.Compliance characteristics are established based on the stiffness matrix method for four different planar flexure layouts.One layout with best in-plane rotational compliance is then assessed for performance sensitivity to mechanism dimension parameters and parasitic error,thus informing the design space.Rotational stiffness in both the inplane rotational axes and stress is determined based on finite element analysis(FEA).The wire electrical discharge machining(EDM)is employed for developing the proof of concept for the RPM and is then assembled in FSM.Experiments are conducted to determine the rotational stiffness and angular travel about both in-plane rotational axes.Comparison among theoretical,numerical and experiments reveal excellent linearity of rotational stiffness along the rotational travel range.The maximum theoretical error is less than 5.5%compared with FEA while,the experimental error has a mean of 5%and 3%for both rotational axes thus satisfying the intended design requirement.展开更多
Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite struc...Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.展开更多
A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been...A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.展开更多
Contraction joint shear keys are resilient features of gravity dams that can be considered to increase the sliding safety factors or minimise seismic residual sliding displacements,allowing costly remedial actions to ...Contraction joint shear keys are resilient features of gravity dams that can be considered to increase the sliding safety factors or minimise seismic residual sliding displacements,allowing costly remedial actions to be avoided.This paper presents a novel,robust,and computationally efficient three-dimensional(3D)modelling and simulation strategy of gravity dams,using a series of adjacent cantilever beam elements to represent individual monoliths.These monoliths are interconnected in the longitudinal direction by 3D no-tension link elements representing the lumped shear key stiffness contributions at a particular elevation.The objective is to assess the shear key internal force demands,including the axial force,shear,and moment demands.Shear key demand-capacity ratios can then be assessed with related multi-axial failure envelopes.The 3D link element stiffness coefficients were derived from a series of 3D finite element(FE)solid models with a detailed representation of geometrical features of multiple shear keys.The results from the proposed method based on advanced grillage analysis show strong agreement with reference solutions from 3D FE solid models,demonstrating high accuracy and performance of the proposed method.The application of the proposed advanced grillage method to a dam model with two monoliths clearly shows the advantage of the proposed method,in comparison to the classical approach used in practise.展开更多
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 61174094）, and the Tianjin Natural Science Foundation of China under （14JCYBJC18700 and 13JCY- BJC17400）.
文摘This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata （DFA） and nondeterministic finite automata （NFA）.
基金Project (No. 03-02-02-0056 PR0025/04-03) supported by Ministry of Science, Technology and Innovation, Malaysia
文摘This paper presents the effects of surface finish and treatment on the high cycle fatigue behaviour of vibrating cylinder block of a new two-stroke free piston engine at complex variable amplitude loading conditions using frequency response approach. Finite element modelling and frequency response analysis was conducted using finite element analysis software Package MSC.PATRAN/MSC.NASTRAN and fatigue life prediction was carded out using MSC.FATIGUE software. Based on the finite element results, different frequency response approach was applied to predict the cylinder block fatigue life. Results for different load histories and material combinations are also discussed. Results indicated great effects for all surface finish and treatment. It is concluded that polished and cast surface finish conditions give the highest and lowest cylinder block lives, respectively; and that Nitrided treatment leads to longest cylinder block life. The results were used to draw contour plots of fatigue life and damage in the worst or most damaging case.
文摘The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using the 20-node solid elements is generated. A linear elastic finite element analysis was performed, hotspot stresses in a web-frame joint were analyzed and fatigue damage was quantified employing the S-N approach. The statistical descriptors of the fatigue life of a non-correlated web-frame joint containing several critical hotspots were estimated. The fatigue reliability of a web-frame joint wasmodeled as a series system of correlated components using the Ditlevsen bounds. The fatigue reliability of the entire welded structure with multiple web-frame joints, modeled as a parallel system of non-correlated web-frame joints was also calculated.
文摘Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.
文摘A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that the new insights may be taken into account as decision points to outperform the available materials. It is to note that the traditional control approaches may generally be upgraded, as long as a number of modifications are made with respect to state-of-the-art, in order to propose high-precision outcomes. Regarding the investigated issues, the robust sliding mode finite-time control approach is first designed to handle three-axis angular rates in the inner control loop, which consists of the pulse width pulse frequency modulations in line with the control allocation scheme and the system dynamics. The main subject to employ these modulations that is realizing in association with the control allocation scheme is to be able to handle a class of overactuated systems, in particular. The proportional derivative based linear quadratic regulator approach is then designed to handle three-axis rotational angles in the outer control loop, which consists of the system kinematics that is correspondingly concentrated to deal with the quaternion based model. The utilization of the linear and its nonlinear terms, simultaneously, are taken into real consideration as the research motivation, while the performance results are of the significance as the improved version in comparison with the recent investigated outcomes. Subsequently, there is a stability analysis to verify and guarantee the closed loop system performance in coping with the whole of nominal referenced commands. At the end, the effectiveness of the approach considered here is highlighted in line with a number of potential recent benchmarks.
基金supported by the National Natural Science Foundation of China(Grant Nos.11672153,11232008 & 11227801)
文摘Residual stress plays a vital role in the structural strength and stability. The determination of residual stress at single-point has become mature at present. However, the method to determine residual stress distribution is still in shortage. For this problem, a finite element approach combined with slot milling method was developed in this study. In the method, firstly a slot is milled on the specimen surface to release the residual stress and then the released displacement field is measured by optical method, such as digital image correlation （DIC）, finally the finite element approach is used to determine the residual stress distribution along the slot. In order to verify the feasibility of the method, it was applied to study the residual stress introduced by shot peening, mainly about the stress distribution along the direction vertical to the shot peened surface. Since the influence depth of shot peening was too small, we utilized focused ion beam （FIB） to determine the microscale residual stress distribution. The result measured by X-ray diffraction （XRD） demonstrated that the method was feasible to determine the residual stress distribution.
基金co-supported by the National Natural Science Foundation of China(No.91748205 and 51675032)the Fundamental Research Funds for the Central Universities(No.YWF-18-BJ-Y-34 and YWF-18-BJ-J-23)of China。
文摘In this paper,a novel 2-DOF rotational pointing mechanism(RPM)is designed inspired by the guidelines of the graphical approach.The mechanism integrates with a fast steering mirror(FSM)for compensating pointing errors of a laser beam.The design intends to achieve an angular travel of±10 mrad and steers a 25 mm mirror aperture.A planar flexure with beam flexures accompanied in parallel with an axial flexure build-up mechanism configuration.Compliant mechanismbased RPM ensures high precision and compactness.Compliance characteristics are established based on the stiffness matrix method for four different planar flexure layouts.One layout with best in-plane rotational compliance is then assessed for performance sensitivity to mechanism dimension parameters and parasitic error,thus informing the design space.Rotational stiffness in both the inplane rotational axes and stress is determined based on finite element analysis(FEA).The wire electrical discharge machining(EDM)is employed for developing the proof of concept for the RPM and is then assembled in FSM.Experiments are conducted to determine the rotational stiffness and angular travel about both in-plane rotational axes.Comparison among theoretical,numerical and experiments reveal excellent linearity of rotational stiffness along the rotational travel range.The maximum theoretical error is less than 5.5%compared with FEA while,the experimental error has a mean of 5%and 3%for both rotational axes thus satisfying the intended design requirement.
基金This work was supported by National Natural Science Foundation of China under Grant 11672266.
文摘Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.
文摘A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.
文摘Contraction joint shear keys are resilient features of gravity dams that can be considered to increase the sliding safety factors or minimise seismic residual sliding displacements,allowing costly remedial actions to be avoided.This paper presents a novel,robust,and computationally efficient three-dimensional(3D)modelling and simulation strategy of gravity dams,using a series of adjacent cantilever beam elements to represent individual monoliths.These monoliths are interconnected in the longitudinal direction by 3D no-tension link elements representing the lumped shear key stiffness contributions at a particular elevation.The objective is to assess the shear key internal force demands,including the axial force,shear,and moment demands.Shear key demand-capacity ratios can then be assessed with related multi-axial failure envelopes.The 3D link element stiffness coefficients were derived from a series of 3D finite element(FE)solid models with a detailed representation of geometrical features of multiple shear keys.The results from the proposed method based on advanced grillage analysis show strong agreement with reference solutions from 3D FE solid models,demonstrating high accuracy and performance of the proposed method.The application of the proposed advanced grillage method to a dam model with two monoliths clearly shows the advantage of the proposed method,in comparison to the classical approach used in practise.
