Introduction to the Finite Element Method Using BASIC Programs.

Cover -- Half Title -- Dedication -- Title Page -- Copyright Page -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- Appendix 1.1 Suggested further reading -- Basic equations -- Matrix Methods -- Computer Routines -- Energy Methods -- Finite Element Analysis -- Appendix 1.2 Introducing the finite element method-crossing bridges in understanding -- Background -- Aims, Objectives and Assessment -- Education -- Training -- 2 PJFRAME: Pin-jointed plane frames -- 2.0 Introduction -- 2.1 Example of truss -- 2.1.1 Application of equilibrium -- 2.1.2 Conditions for geometric compatibility -- 2.1.3 Stress/strain or force/elongation relations -- 2.1.4 Boundary conditions and solution -- 2.2 The pin-jointed element -- 2.2.1 Direction cosines -- 2.2.2 Procedure in applying stiffness method to a pin-jointed structure -- 2.2.3 Solution of truss in Fig 2.10 using the stiffness method -- 2.2.4 Load vector {P} -- 2.2.5 Nodal forces and reactions -- 2.3 Implementation in program -- 2.3.1 Description of program -- 2.3.2 Data preparation -- 2.3.3 Program PJFRAME -- 2.3.4 Example of truss analysis using PJFRAME -- Appendix 2.1 PJFRAME: Program summary and data sheet -- 1. Introduction -- 2. Datasheet for PJFRAME -- 3 PLFRAME: Rigid/pin-jointed plane frames -- 3.0 Introduction -- 3.1 Development of equations -- 3.1.1 Stiffness matrix about member axis -- 3.1.2 Application of equations (3.12) to a simple orthogonal structure -- 3.1.3 Transforming the member stiffness matrix [K'] from local to global coordinates -- 3.1.4 Example -- 3.1.5 Dealing with different end conditions -- 3.1.6 Dealing with member loads -- 3.2 Implementation in program -- 3.2.1 Description of program -- 3.2.2 Data preparation -- 3.2.3 Program PLFRAME -- 3.2.4 Example of plane frame analysis using PLFRAME -- Appendix 3.1 PLFRAME: Program summary and data sheet -- 1. Introduction.

2. Datasheet for PLFRAME -- Appendix 3.2 Alternative approach to finding the stiffness matrix -- 4 FEPCST: Plane stress/plane strain finite element analysis using constant strain triangles -- 4.0 Introduction -- 4.1 Development of equations -- 4.1.1 The stiffness coefficients for a general triangular plane stress/plane strain element -- 4.2 Illustrative example -- 4.2.1 Using element stiffness matrices -- 4.2.2 Using potential energy applied to the whole structure -- 4.3 Implementation in program -- 4.3.1 Description of program -- 4.3.2 Data preparation -- 4.3.3 Program FEPCST -- 4.3.4 Example of solution to continuum problem using FEPCST -- Appendix 4.1 FEPCST: Program summary and data sheet -- 1. Introduction -- 2. Datasheet for FEPCST -- 5 FEPB: Bending of thin flat plates -- 5.0 Introduction -- 5.1 Development of equations -- 5.1.1 Finite element method - rectangular element -- 5.1.2 Determination of triple product -- 5.1.3 Assemblage and solution -- 5.2 Implementation in program -- 5.2.1 Description of program -- 5.2.2 Data preparation -- 5.2.3 Program FEPB -- 5.2.4 Example of solution to thin rectangular plate problem using FEPB -- Appendix 5.1 FEPB: Program summary and data sheet -- 1. Introduction -- 2. Datasheet for FEPB -- 6 FEPLST: Plane stress/strain finite element analyses using linear strain triangles -- 6.0 Introduction -- 6.1 Generalized coordinate displacement models -- 6.2 Interpolation displacement models -- 6.2.1 Triangular coordinate system -- 6.2.2 Examples of interpolation displacement models -- 6.3 Interpolation models for a triangle -- 6.3.1 Linear interpolation function -- 6.3.2 Quadratic interpolation function -- 6.4 Elements with curved sides -- 6.5 Developing the stiffness matrix -- 6.5.1 Determining stresses and strains -- 6.5.2 Deriving the stiffness matrix.

6.5.3 Constant strain triangle (CST) - linear displacement model -- 6.5.4 Linear strain triangle (LST) - quadratic displacement model -- 6.6 Summary of procedure to determine [K] for the straight-sided LST -- 6.7 Load vector {P} for CST and LST -- 6.8 Implementation in program -- 6.8.1 Description of program -- 6.8.2 Data preparation -- 6.8.3 Program FEPLST -- 6.8.4 Example of solution of continuum problem using FEPLST -- Appendix 6.1 FEPLST: Program summary and data sheet -- 1. Introduction -- 2. Datasheet for FEPLST -- 7 The linear isoparametric quadrilateral element -- 7.0 Introduction -- 7.1 The interpolation displacement model -- 7.1.1 Rectangular coordinate system -- 7.1.2 Linear interpolation function -- 7.2 Determination of strains -- 7.2.1 Establishing the derivatives ∂N/∂s and ∂N/∂t -- 7.2.2 Establishing the derivatives ∂s/∂x and ∂s/∂y etc. -- 7.3 Determination of stresses -- 7.4 Determination of the stiffness matrix -- 7.4.1 Establishing the general form of [K] -- 7.4.2 Numerical integration -- 7.4.3 Formation of the triple product [B]T[D] [B] -- 7.5 Load vector {P} -- 8 The quadratic isoparametric quadrilateral -- 8.0 Introduction -- 8.1 Quadratic interpolation model -- 8.2 Determination of strains -- 8.3 Determination of stresses -- 8.4 Determination of stiffness matrix -- 8.5 Load vector {P} -- 8.6 Example of single element check on stiffness matrix -- (a) Longhand solution -- (b) Finite element solution -- 9 Further developments of programs -- 9.0 Introduction -- 9.1 Possible developments -- 9.1.1 Units -- 9.1.2 Increasing the number of elements and nodes -- 9.1.3 Data through INPUT statements -- 9.1.4 Plotting of grids -- 9.1.5 Multiple load cases -- 9.1.6 Efficient storage -- 9.1.7 The use of disc storage -- Appendix A Matrix algebra -- A.1 Matrix properties and manipulations -- A.1.1 Definitions -- A.1.2 Transpose.

A.1.3 Addition and subtraction -- A.1.4 Multiplication -- A.1.5 Transpose of a product -- A.1.6 Determinant -- A.1.7 Inverse of a matrix -- A.1.8 System of equations -- A.1.9 Matrix integration and differentiation -- A.2 Structural stiffness matrices -- A.2.1 More efficient storage -- A.2.2 Equation solution procedures -- Appendix B Basic: ours and yours (by D.A. Pirie) -- B.1 Why BASIC? -- B.1.1 Portable BASIC -- B.1.2 Formatting of results -- B.2 Our BASIC -- B.2.1 Data types -- B.2.2 Program elements - constants, variables, expressions -- B.2.3 Line numbering, types of program statement -- B.3 Use of formatting subroutines -- B.4 Your BASIC -- Appendix C Energy method of structural analysis -- C.1 Introduction -- C.2 Application to beam problems -- C.2.1 Principle of virtual work -- C.2.2 Dual energy theorems - complementary and potential -- C.3 Application to continuum problems -- C.3.1 Statement of virtual work equation -- C.3.2 Statement of potential energy functional -- C.4 Note on bounding energy solution -- C.4.1 Statement of potential energy functional for pin-jointed frames -- C.4.2 Example of use of potential energy for trusses -- Index.

This updated, revised and extended edition gives a comprehensive introduction to the understanding and use of the finite element method as applied to structures. The text methodically covers all the important bridges in understanding up to and including the introduction of isoparametric elements.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.