In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduc...A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduced and successfully applied to complex contact friction problem.Test example and actual engineering case all show that the algorithm of the model is efficient and computation results agree well with general rules.展开更多
Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model ba...Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.展开更多
We formulate a Lagrange method for continuous-time stochastic optimization in an appropriate normed space by using a proper stochastic process as the Lagrange multiplier.The obtained optimality conditions are applied ...We formulate a Lagrange method for continuous-time stochastic optimization in an appropriate normed space by using a proper stochastic process as the Lagrange multiplier.The obtained optimality conditions are applied to different types of problems.Some examples selected from control theory and economic theory are studied to test and illustrate the potential applications of the method.展开更多
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad...In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.展开更多
The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisi...The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.展开更多
This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the...This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.展开更多
In the paper, the problems of dynamie response of multi-rigidbody systems with external impulsive forces are diseussed, and a set of equations with form of Lagrange method is presented. These equations are easy to be ...In the paper, the problems of dynamie response of multi-rigidbody systems with external impulsive forces are diseussed, and a set of equations with form of Lagrange method is presented. These equations are easy to be caleulated by computer.展开更多
In recent decades,the cloud computing contributes a prominent role in health care sector as the patient health records are transferred and collected using cloud computing services.The doctors have switched to cloud co...In recent decades,the cloud computing contributes a prominent role in health care sector as the patient health records are transferred and collected using cloud computing services.The doctors have switched to cloud computing as it provides multiple advantageous measures including wide storage space and easy availability without any limitations.This necessitates the medical field to be redesigned by cloud technology to preserve information about patient’s critical diseases,electrocardiogram(ECG)reports,and payment details.The proposed work utilizes a hybrid cloud pattern to share Massachusetts Institute of Technology-Beth Israel Hospital(MIT-BIH)resources over the private and public cloud.The stored data are categorized as significant and non-significant by Artificial Neural Networks(ANN).The significant data undergoes encryption by Lagrange key management which automatically generates the key and stores it in the hidden layer.Upon receiving the request from a secondary user,the primary user verifies the authentication of the request and transmits the key via Gmail to the secondary user.Once the key matches the key in the hidden layer,the preserved information will be shared between the users.Due to the enhanced privacy preserving key generation,the proposed work prevents the tracking of keys by malicious users.The outcomes reveal that the introduced work provides improved success rate with reduced computational time.展开更多
Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front...Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.展开更多
Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on seco...Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.展开更多
Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacemen...Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
This paper presents a hydrodynamic analysis of a hybrid system consisting of a floating platform coupled with an array of oscillating bodies that move along the weather sidewall of the platform.Using the Lagrange mult...This paper presents a hydrodynamic analysis of a hybrid system consisting of a floating platform coupled with an array of oscillating bodies that move along the weather sidewall of the platform.Using the Lagrange multiplier method,the motion equation governing this type of motion characteristic is formulated,and the formula of the extracted wave power is derived.The numerical results demonstrate a significant increase in the hydrodynamic efficiency of oscillating bodies within specific frequency ranges in the presence of the floating platform.The incorporation of proper power take-off damping of the oscillating bodies results in a reduction in the heave motion of the platform,but it may lead to an increase in pitch motion.The analysis of the response behaviour of the system shows that both the heave motion and pitch motion of the platform contribute to the power extraction and relative motion between the buoys and the platform.Parametric investigations are conducted to explore the hydrodynamic interactions between the floating platform and the buoy array.Additionally,the concept of“hydrodynamic synergy”is proposed to describe the synergetic effect of different components of a multi-purpose platform,which is of considerable engineering interest.展开更多
Contact nonlinear theory was researched. Contact problem was transformed into optimization problem containing Lagrange multiplier, and unsymmetrical stiffness matrix was transformed into symmetrical stiffness matrix. ...Contact nonlinear theory was researched. Contact problem was transformed into optimization problem containing Lagrange multiplier, and unsymmetrical stiffness matrix was transformed into symmetrical stiffness matrix. A finite element analysis （FEA） model defining more than 300 contact pairs for long nut-short screw locking mechanism of a large-scale vertical gear-rack typed ship-lift was built. Using augmented Lagrange method and symmetry algorithm of contact element stiffness, the FEA model was analyzed, and the contact stress of contact interfaces and the von Mises stress of key parts were obtained. The results show that the design of the locking mechanism meets the requirement of engineering, and this method is effective for solving large stole nonlinear contact pairs.展开更多
Humanoid robots are a hot topic in the field of robotics research. The walking system is the critical part of the humanoid robot, and the dynamic simulation of the walking system is of great importance. In this paper,...Humanoid robots are a hot topic in the field of robotics research. The walking system is the critical part of the humanoid robot, and the dynamic simulation of the walking system is of great importance. In this paper, the stability of the walking system and the rationality of its structural design are considered in the study of dynamics for a humanoid robot. The dynamic model of humanoid robot walking system is established by using the Lagrange dynamics method. Additionally, the three-dimensional model of CATIA is imported into ADAMS. The humanoid robot walking system is added with the movement of the deputy and the driving force in the ADAMS.The torque and angular velocity of the ankle joint and hip joint are analyzed in the process of knee bends. The simulation results show that the overall performance of the humanoid robot walking system is favorable and has a smooth movement, and the specified actions can be completed, which proves the rationality of the humanoid robot walking system design.展开更多
Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor...Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system are divided into three kinds： additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2x excitation force might appear.展开更多
Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During t...Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.展开更多
There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method...There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.展开更多
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduced and successfully applied to complex contact friction problem.Test example and actual engineering case all show that the algorithm of the model is efficient and computation results agree well with general rules.
文摘Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.
基金supported by National Natural Science Foundation of China (Grant No.11001029)the National Basic Research Program of China (973 Program) (Grant No. 2007CB814902)+1 种基金the Science Fund for Creative Research Groups (Grant No. 11021161)Key Laboratory of Random Complex Structures and Data Science (Grant No. 2008DP173182)
文摘We formulate a Lagrange method for continuous-time stochastic optimization in an appropriate normed space by using a proper stochastic process as the Lagrange multiplier.The obtained optimality conditions are applied to different types of problems.Some examples selected from control theory and economic theory are studied to test and illustrate the potential applications of the method.
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
基金Supported by National Natural Science Foundation of China (No.51275348)College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339)
文摘In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
文摘The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.
基金This study is supported by the National Natural Science Foundation of China (Grant No50579046) the Science Foundation of Tianjin Municipal Commission of Science and Technology (Grant No043114711)
文摘This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.
文摘In the paper, the problems of dynamie response of multi-rigidbody systems with external impulsive forces are diseussed, and a set of equations with form of Lagrange method is presented. These equations are easy to be caleulated by computer.
文摘In recent decades,the cloud computing contributes a prominent role in health care sector as the patient health records are transferred and collected using cloud computing services.The doctors have switched to cloud computing as it provides multiple advantageous measures including wide storage space and easy availability without any limitations.This necessitates the medical field to be redesigned by cloud technology to preserve information about patient’s critical diseases,electrocardiogram(ECG)reports,and payment details.The proposed work utilizes a hybrid cloud pattern to share Massachusetts Institute of Technology-Beth Israel Hospital(MIT-BIH)resources over the private and public cloud.The stored data are categorized as significant and non-significant by Artificial Neural Networks(ANN).The significant data undergoes encryption by Lagrange key management which automatically generates the key and stores it in the hidden layer.Upon receiving the request from a secondary user,the primary user verifies the authentication of the request and transmits the key via Gmail to the secondary user.Once the key matches the key in the hidden layer,the preserved information will be shared between the users.Due to the enhanced privacy preserving key generation,the proposed work prevents the tracking of keys by malicious users.The outcomes reveal that the introduced work provides improved success rate with reduced computational time.
文摘Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.
基金supported by the National Natural Science Foundation of China (11002075 and 10972110)
文摘Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.
基金supported by the China Postdoctoral Science Foundation Funded Project (20080430038) the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (05004999200602)
文摘Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
基金supported by the National Key Research and Development Project of China(Grant No.2023YFC3106904)National Natural Science Foundation of China(Grant No.52001086)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.3072023JC0101)Additionally,this work contributes to the Strategic Research Plan of the Centre for Marine Technology and Ocean Engineering(CENTEC),which is financed by the Portuguese Foundation for Science and Technology(Fundação para a Ciência e Tecnologia-FCT)under contract UIDB/UIDP/00134/2020.
文摘This paper presents a hydrodynamic analysis of a hybrid system consisting of a floating platform coupled with an array of oscillating bodies that move along the weather sidewall of the platform.Using the Lagrange multiplier method,the motion equation governing this type of motion characteristic is formulated,and the formula of the extracted wave power is derived.The numerical results demonstrate a significant increase in the hydrodynamic efficiency of oscillating bodies within specific frequency ranges in the presence of the floating platform.The incorporation of proper power take-off damping of the oscillating bodies results in a reduction in the heave motion of the platform,but it may lead to an increase in pitch motion.The analysis of the response behaviour of the system shows that both the heave motion and pitch motion of the platform contribute to the power extraction and relative motion between the buoys and the platform.Parametric investigations are conducted to explore the hydrodynamic interactions between the floating platform and the buoy array.Additionally,the concept of“hydrodynamic synergy”is proposed to describe the synergetic effect of different components of a multi-purpose platform,which is of considerable engineering interest.
基金Supported by the Key Research Project of StatePower Corporation (SPKJ 0l6-06)the Key Scientific ResearchProject of Hubei Province ( 2004AC101D31)
文摘Contact nonlinear theory was researched. Contact problem was transformed into optimization problem containing Lagrange multiplier, and unsymmetrical stiffness matrix was transformed into symmetrical stiffness matrix. A finite element analysis （FEA） model defining more than 300 contact pairs for long nut-short screw locking mechanism of a large-scale vertical gear-rack typed ship-lift was built. Using augmented Lagrange method and symmetry algorithm of contact element stiffness, the FEA model was analyzed, and the contact stress of contact interfaces and the von Mises stress of key parts were obtained. The results show that the design of the locking mechanism meets the requirement of engineering, and this method is effective for solving large stole nonlinear contact pairs.
基金the Jilin Province Science and Technology Development Project(No.20150309005YY)the National Natural Science Foundation of China(No.51875047)
文摘Humanoid robots are a hot topic in the field of robotics research. The walking system is the critical part of the humanoid robot, and the dynamic simulation of the walking system is of great importance. In this paper, the stability of the walking system and the rationality of its structural design are considered in the study of dynamics for a humanoid robot. The dynamic model of humanoid robot walking system is established by using the Lagrange dynamics method. Additionally, the three-dimensional model of CATIA is imported into ADAMS. The humanoid robot walking system is added with the movement of the deputy and the driving force in the ADAMS.The torque and angular velocity of the ankle joint and hip joint are analyzed in the process of knee bends. The simulation results show that the overall performance of the humanoid robot walking system is favorable and has a smooth movement, and the specified actions can be completed, which proves the rationality of the humanoid robot walking system design.
文摘Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system are divided into three kinds： additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2x excitation force might appear.
基金Supported by the Fundamental Research Funds for the Central Universities of China (2009QL05)
文摘Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.
基金subsidized by special funds for the National Basic Research Program of China (No.2002cb412708)supported by the Opening Funds of the State Key Laboratory of Hydroscience and Engineering of China (No.sklhse-2007-D-02)
文摘There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.
