The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a sp...The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.展开更多
Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a ...Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.展开更多
Idioms,collocations,and formulaic phrases are three factors playing the important role in the second language acquisition(SLA).This essay firstly deals with the definitions of these concepts,then it illustrates the im...Idioms,collocations,and formulaic phrases are three factors playing the important role in the second language acquisition(SLA).This essay firstly deals with the definitions of these concepts,then it illustrates the importance of them to SLA on two perspectives—idioms,collocations,and formulaic phrases respectively and they regarded as a whole.Therefore,in this way,the essay may lead to the answer the question“How are idioms,collocations,and formulaic phrases important to SLA?”展开更多
Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitar...Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.展开更多
The piezothermoelectric actuator/sensor collocation for advanced intelligent structure is studied. The quasi-static equations of piezothermoelasticity are used to analyze the coupling effects between the displaceme...The piezothermoelectric actuator/sensor collocation for advanced intelligent structure is studied. The quasi-static equations of piezothermoelasticity are used to analyze the coupling effects between the displacement, temperature and electric fields of piezothermoelasticity continua and the governing equations for piezothermoelasticity continua are derived to discuss the effects of coupling factors on the control/sensing performance in intelligent structure. Based on those analyses, a finite element analysis model of distributed piezothertnoelectric continua is developed later. The thermal stress and deformation of a beam are calculated by FEA method so as to determine the optimal actuator/sensor placement. Based on the results of the optimal analysis procedure of actuator/sensor placement, some conclusions of actuator/sensor placement are obtained. Thus, the optimal actuator/sensor placement for piezothermoelectric intelligent structure can be found from the actuator/sensor placements available so that intelligent system will have the best controllability and observability.展开更多
In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This k...In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.展开更多
In this work, we have obtained numerical solutions of the generalized Korteweg-de Vries (GKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by ap...In this work, we have obtained numerical solutions of the generalized Korteweg-de Vries (GKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying test problems including;single soliton wave. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms, <em>L</em><sub>2</sub> and <em>L</em><sub>∞</sub> and invariants <em>I</em><sub>1</sub>, <em>I</em><sub>2</sub> and <em>I</em><sub>3</sub> have been calculated. Our numerical results are compared with some of those available in the literature.展开更多
文摘The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.
文摘Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.
文摘Idioms,collocations,and formulaic phrases are three factors playing the important role in the second language acquisition(SLA).This essay firstly deals with the definitions of these concepts,then it illustrates the importance of them to SLA on two perspectives—idioms,collocations,and formulaic phrases respectively and they regarded as a whole.Therefore,in this way,the essay may lead to the answer the question“How are idioms,collocations,and formulaic phrases important to SLA?”
文摘Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.
基金The project is supported by National Natural Science Foundation of China (59805018)
文摘The piezothermoelectric actuator/sensor collocation for advanced intelligent structure is studied. The quasi-static equations of piezothermoelasticity are used to analyze the coupling effects between the displacement, temperature and electric fields of piezothermoelasticity continua and the governing equations for piezothermoelasticity continua are derived to discuss the effects of coupling factors on the control/sensing performance in intelligent structure. Based on those analyses, a finite element analysis model of distributed piezothertnoelectric continua is developed later. The thermal stress and deformation of a beam are calculated by FEA method so as to determine the optimal actuator/sensor placement. Based on the results of the optimal analysis procedure of actuator/sensor placement, some conclusions of actuator/sensor placement are obtained. Thus, the optimal actuator/sensor placement for piezothermoelectric intelligent structure can be found from the actuator/sensor placements available so that intelligent system will have the best controllability and observability.
文摘In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.
文摘In this work, we have obtained numerical solutions of the generalized Korteweg-de Vries (GKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying test problems including;single soliton wave. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms, <em>L</em><sub>2</sub> and <em>L</em><sub>∞</sub> and invariants <em>I</em><sub>1</sub>, <em>I</em><sub>2</sub> and <em>I</em><sub>3</sub> have been calculated. Our numerical results are compared with some of those available in the literature.
