... Those mission concepts include plans for Mars missions, sample return missions for Venus and ... more ... Those mission concepts include plans for Mars missions, sample return missions for Venus and a comet nucleus, Europa orbiter and lander missions, a Titan organics explorer, and a terrestrial planet finder. PMID: 11542653 [PubMed - indexed for MEDLINE]. MeSH Terms: ...
Page 1. Engineering with Computers 3,225-241 (1988) Engineering computers 9 Springer-Verlag New Y... more Page 1. Engineering with Computers 3,225-241 (1988) Engineering computers 9 Springer-Verlag New York Inc. 1988 Parallel Processing in Finite Element Structural Analysis Ahmed K. Noor George Washington University, NASA Langley Research Center, Hampton, Virginia ...
A simple penalty finite element formulation is presented for the large‐rotation and postbuckling ... more A simple penalty finite element formulation is presented for the large‐rotation and postbuckling analyses of curved beams. The analytical formulation is based on a form of Reissner's large‐deformation theory with the transverse shear deformation and the extensibility of the center line constrained through the use of the penalty method. Reduced integration is used in evaluating the elemental arrays, and a procedure is outlined for determining the critical points in the solution path. Numerical results are presented to demonstrate the effectiveness of the finite elements developed.
A two-dimensional computational model is developed for nonlinear heat transfer in multilayered co... more A two-dimensional computational model is developed for nonlinear heat transfer in multilayered composite panels. The model is based on a first-order thermal lamination theory with a linear through-the-thickness variation of temperature. Both convection and nonlinear conduction modes of heat transfer are considered. A three-field mixed finite element model is used for the spatial discretization, with the fundamental unknowns consisting of temperature parameters, flux resultants, and generalized temperature gradients. The flux resultants and generalized temperature gradients are eliminated on the element level. A computational procedure is presented for generating the thermal response and the sensitivity derivatives with respect to material and lamination parameters. The effectiveness of the foregoing two-dimensional computational model is demonstrated by means of two numerical examples in which the solutions obtained by the model are compared with three-dimensional finite element solutions.
An efficient computational procedure is presented for the analysis of laminated anisotropic shell... more An efficient computational procedure is presented for the analysis of laminated anisotropic shells of revolution and assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory, including the effects of both the transverse shear deformation and the laminated anisotropic material response. Each of the shell variables is expanded in a Fourier series in the circumferential coordinate, and a two‐field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (1) use of mixed finite element models in the meridional direction with discontinuous stress resultants at the element interfaces; (2) operator splitting, or decomposition of the material compliance matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) part; and (3) application of a reduction method through the successive use of the...
International Journal for Numerical Methods in Engineering, 1987
A simple computational procedure is presented for reducing the size of the analysis model for a s... more A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh–Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh–Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The gl...
International Journal for Numerical Methods in Engineering, 1981
Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A tota... more Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger–Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries.The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical resul...
International Journal for Numerical Methods in Engineering, 1987
An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are ... more An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non‐orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
A two‐step computational procedure is presented for reducing the size of the analysis model for a... more A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh—Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding ...
... Printed in Great Britain MIXED FINITE-DIFFERENCE SCHEME FOR ANALYSIS OF SIMPLY SUPPORTED THIC... more ... Printed in Great Britain MIXED FINITE-DIFFERENCE SCHEME FOR ANALYSIS OF SIMPLY SUPPORTED THICK PLATES AHMED K. NooRf George Washington University Center, NASA ... 967 968 n {} [] AHMED K. NOOR row matrix column matrix rectangular or square matrix. ...
Abstract An algorithm is presented for the evaluation of the stiffness matrices of higher-order e... more Abstract An algorithm is presented for the evaluation of the stiffness matrices of higher-order elements on the CDC STAR-100 computer. Discussion is focused on the organization of the computation and the mode of storage of the different arrays to take advantage of the STAR pipeline (streaming) capability. An assessment is made of the performance of the proposed algorithm for generating the stiffness matrices of two higher order composite shallow shell and plate elements having 80 and 176 degrees of freedom. Also, estimates are given of the CPU times required to evaluate the stiffness coefficients of three-dimensional hexahedral elements using the proposed algorithm.
Status and some recent advances in the application of reduction methods to instability analysis o... more Status and some recent advances in the application of reduction methods to instability analysis of structures are summarized. The aspects of reduction methods discussed herein include: (a) multiple-parameter reduction methods for instability analysis of structures subjected to ...
... Noor. JH Starnes, Jr and JM Peters, Non linear and postbuckling responses of curved composite... more ... Noor. JH Starnes, Jr and JM Peters, Non linear and postbuckling responses of curved composite panels with cutouts. In Proc. 36th AIAA I ASME I ASCE AHS ASC Structures, Structural Dynamics and Materials Conf., New Orleans, LA, 1013 April, Collec tion of Technical Papers ...
The potential of using computerized symbolic manipulation in the development of nonlinear finite ... more The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness ...
... Those mission concepts include plans for Mars missions, sample return missions for Venus and ... more ... Those mission concepts include plans for Mars missions, sample return missions for Venus and a comet nucleus, Europa orbiter and lander missions, a Titan organics explorer, and a terrestrial planet finder. PMID: 11542653 [PubMed - indexed for MEDLINE]. MeSH Terms: ...
Page 1. Engineering with Computers 3,225-241 (1988) Engineering computers 9 Springer-Verlag New Y... more Page 1. Engineering with Computers 3,225-241 (1988) Engineering computers 9 Springer-Verlag New York Inc. 1988 Parallel Processing in Finite Element Structural Analysis Ahmed K. Noor George Washington University, NASA Langley Research Center, Hampton, Virginia ...
A simple penalty finite element formulation is presented for the large‐rotation and postbuckling ... more A simple penalty finite element formulation is presented for the large‐rotation and postbuckling analyses of curved beams. The analytical formulation is based on a form of Reissner's large‐deformation theory with the transverse shear deformation and the extensibility of the center line constrained through the use of the penalty method. Reduced integration is used in evaluating the elemental arrays, and a procedure is outlined for determining the critical points in the solution path. Numerical results are presented to demonstrate the effectiveness of the finite elements developed.
A two-dimensional computational model is developed for nonlinear heat transfer in multilayered co... more A two-dimensional computational model is developed for nonlinear heat transfer in multilayered composite panels. The model is based on a first-order thermal lamination theory with a linear through-the-thickness variation of temperature. Both convection and nonlinear conduction modes of heat transfer are considered. A three-field mixed finite element model is used for the spatial discretization, with the fundamental unknowns consisting of temperature parameters, flux resultants, and generalized temperature gradients. The flux resultants and generalized temperature gradients are eliminated on the element level. A computational procedure is presented for generating the thermal response and the sensitivity derivatives with respect to material and lamination parameters. The effectiveness of the foregoing two-dimensional computational model is demonstrated by means of two numerical examples in which the solutions obtained by the model are compared with three-dimensional finite element solutions.
An efficient computational procedure is presented for the analysis of laminated anisotropic shell... more An efficient computational procedure is presented for the analysis of laminated anisotropic shells of revolution and assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory, including the effects of both the transverse shear deformation and the laminated anisotropic material response. Each of the shell variables is expanded in a Fourier series in the circumferential coordinate, and a two‐field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (1) use of mixed finite element models in the meridional direction with discontinuous stress resultants at the element interfaces; (2) operator splitting, or decomposition of the material compliance matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) part; and (3) application of a reduction method through the successive use of the...
International Journal for Numerical Methods in Engineering, 1987
A simple computational procedure is presented for reducing the size of the analysis model for a s... more A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh–Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh–Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The gl...
International Journal for Numerical Methods in Engineering, 1981
Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A tota... more Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger–Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries.The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical resul...
International Journal for Numerical Methods in Engineering, 1987
An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are ... more An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non‐orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
A two‐step computational procedure is presented for reducing the size of the analysis model for a... more A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh—Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding ...
... Printed in Great Britain MIXED FINITE-DIFFERENCE SCHEME FOR ANALYSIS OF SIMPLY SUPPORTED THIC... more ... Printed in Great Britain MIXED FINITE-DIFFERENCE SCHEME FOR ANALYSIS OF SIMPLY SUPPORTED THICK PLATES AHMED K. NooRf George Washington University Center, NASA ... 967 968 n {} [] AHMED K. NOOR row matrix column matrix rectangular or square matrix. ...
Abstract An algorithm is presented for the evaluation of the stiffness matrices of higher-order e... more Abstract An algorithm is presented for the evaluation of the stiffness matrices of higher-order elements on the CDC STAR-100 computer. Discussion is focused on the organization of the computation and the mode of storage of the different arrays to take advantage of the STAR pipeline (streaming) capability. An assessment is made of the performance of the proposed algorithm for generating the stiffness matrices of two higher order composite shallow shell and plate elements having 80 and 176 degrees of freedom. Also, estimates are given of the CPU times required to evaluate the stiffness coefficients of three-dimensional hexahedral elements using the proposed algorithm.
Status and some recent advances in the application of reduction methods to instability analysis o... more Status and some recent advances in the application of reduction methods to instability analysis of structures are summarized. The aspects of reduction methods discussed herein include: (a) multiple-parameter reduction methods for instability analysis of structures subjected to ...
... Noor. JH Starnes, Jr and JM Peters, Non linear and postbuckling responses of curved composite... more ... Noor. JH Starnes, Jr and JM Peters, Non linear and postbuckling responses of curved composite panels with cutouts. In Proc. 36th AIAA I ASME I ASCE AHS ASC Structures, Structural Dynamics and Materials Conf., New Orleans, LA, 1013 April, Collec tion of Technical Papers ...
The potential of using computerized symbolic manipulation in the development of nonlinear finite ... more The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness ...
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