Download or read book Integrated Force Method Solution to Indeterminate Structural Mechanics Problems written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-15 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems. Patnaik, Surya N. and Hopkins, Dale A. and Halford, Gary R. Glenn Research Center WBS-22-708-24-08
Download or read book Integrated Force Method Solution to Indeterminate Structural Problems written by Surya Patnaik and published by LAP Lambert Academic Publishing. This book was released on 2010-10 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the 'cutting and closing gap' technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The author has researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM).IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized.
Download or read book Development of Finite Elements for Two Dimensional Structural Analysis Using the Integrated Force Method written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-16 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations. Kaljevic, Igor and Patnaik, Surya N. and Hopkins, Dale A. Glenn Research Center NASA-TM-4655, E-9240, NAS 1.15:4655 RTOP 505-63-53...
Download or read book Improved Accuracy for Finite Element Structural Analysis Via a New Integrated Force Method written by and published by . This book was released on 1992 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Mechanics of Solids written by Lester W. Schmerr and published by Cambridge University Press. This book was released on 2021-02-18 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Build on elementary mechanics of materials texts with this treatment of the analysis of stresses and strains in elastic bodies.
Download or read book Integrated Force Method Versus Displacement Method for Finite Element Analysis written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-05 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost. Patnaik, Surya N. and Berke, Laszlo and Gallagher, Richard H. Glenn Research Center RTOP 505-63-1B...
Download or read book Energy and Finite Element Methods in Structural Mechanics written by IrvingH Shames and published by Routledge. This book was released on 2018-05-08 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.
Download or read book Integrated Force Method Versus Displacement Method for Finite Element Analysis written by Surya N. Patnaik and published by . This book was released on 1990 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Tech Briefs written by and published by . This book was released on 2008 with total page 1144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy and Finite Element Methods In Structural Mechanics written by IrvingH Shames and published by Routledge. This book was released on 2017-09-06 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1996. CRC Press is an imprint of Taylor & Francis.
Download or read book NASA Technical Paper written by and published by . This book was released on 1990 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Strength of Materials written by Surya Patnaik and published by Butterworth-Heinemann. This book was released on 2004 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinate truss -- Simple beam -- Determinate shaft -- Simple frames -- Indeterminate truss -- Indeterminate beam -- Indeterminate shaft -- Indeterminate frame -- Two-dimensional structures -- Column buckling -- Energy theorems -- Finite element method -- Special topics.
Download or read book Finite Element Method written by Sinan Muftu and published by Academic Press. This book was released on 2022-07-14 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Method: Physics and Solution Methods aims to provide the reader a sound understanding of the physical systems and solution methods to enable effective use of the finite element method. This book focuses on one- and two-dimensional elasticity and heat transfer problems with detailed derivations of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. Following the chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing partial differential equation is defined over a subsegment (element) of the solution domain. As well as being a guide to thorough and effective use of the finite element method, this book also functions as a reference on theory of elasticity, heat transfer, and mechanics of beams. Covers the detailed physics governing the physical systems and the computational methods that provide engineering solutions in one place, encouraging the reader to conduct fully informed finite element analysis Addresses the methodology for modeling heat transfer, elasticity, and structural mechanics problems Extensive worked examples are provided to help the reader to understand how to apply these methods in practice
Download or read book Compatibility Conditions of Structural Mechanics for Finite Element Analysis written by and published by . This book was released on 1990 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compatibility Conditions of Structural Mechanics written by Surya N. Patnaik and published by . This book was released on 1999 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elasticity has camouflaged a deficiency in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual "cuts" and closing "gaps" are not parallel to the strain formulation in elasticity. This deficiency in the compatibility conditions has prevented the development of a direct stress determination method in structures and in elasticity. We have addressed this deficiency and attempted to unify the theory of compatibility. This work has led to the development of the integrated force method for structures and the completed Beltrami-Michell formulation for elasticity, The improved accuracy observed in the solution of numerical examples by the integrated force method can be attributed to the compliance of the compatibility conditions. Using the compatibility conditions allows mapping of variables and facile movement among different structural and analysis formulations. This paper reviews and illustrates the requirement of compatibility in structures and in elasticity. It also describes the generation of the conditions and quantifies the benefits of their use. The traditional analysis methods and available solutions (which have been obtained bypassing the missed conditions) should be verified for compliance of the compatibility conditions.
Download or read book Stress Formulation in Three Dimensional Elasticity written by Surya N. Patnaik and published by . This book was released on 2001 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary. the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation : differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1963 with total page 1196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
