برنامه درسی

مطالب درسی تدریسی

هفته

مروری بر مقاومت مصالح درس پیشنیاز -معرفی مراجع درسی،بیان نحوه ارزیابی و تقسیم بندی نمره  در طول ترم، بیان جایگاه و اهمیت درس مقاومت مصالح در  علوم مهندسی، بیان سرفصل های درس- طراحی تیرها و شفتها برای مقاومت

اول

دیاگرام نیروی برشی و گشتاور خمشی- روابط بین بار- نیروی برشی-گشتاور خمشی

دوم

مراحل طراحی تیرهای منشوری

سوم

تغییرشکل تیرها با استفاده از روش انتکرالگیری- مقدمه- منحنی الاستیک تیرها

چهارم

حل مسایل مربوط به تیرهای که از نظر استاتیکی نامعین هستند

پنجم

استفاده ازتوابع تکین برای تحلیل تغییر شکل الاستیکی تیرها

ششم

تعیین تغییر شکل ازطریق توزیع بار(در تیر منشوری همگن)

هفتم

روش جمع آثار برای محاسبه خیز وشیب- محاسبه تغییر شکل تیرها با استفاده از روش گشتاور سطح

هشتم

قضایای گشتاور سطح- کار برد قضیه اول ودوم گشتاور سطح برای تیرهای یک سر گیردار وتیرهای متقارن- تیرها با بارگذاری غیر متقارن

نهم

روشهای انرژی- مقدمه- چگالی انرژی کرنشی- انرژی کرنشی الاستیک برای تنشهای عمودی

دهم

انرژی کرنشی الاستیک تحت اثر بار محوری- انرژی کرنشی الاستیک تحت اثر گشتاور خمشی

یازدهم

انرژی کرنشی الاستیک برای تنشهای برشی- انرژی کرنشی الاستیک برای تنشهای برشی تا حد خطی- انرژی کرنشی الاستیک ناشی از گشتاور پیچشی- انرژی کرنشی الاستیک ناشی از بار برشی

دوازدهم

چگالی انرژی کرنشی برای حالت کلی تنشها- بار گذاری ضربه ای- طراحی در مقابل بارهای دینامیکی

سیزدهم

کار وانرژی تحت تاثیر یک بار- محاسبه تغییر شکل سازه تحت تاثیر یک بار متمرکز با استفاده از رابطه کار وانرژی- کار وانرژی تحت اثر چندین بار- قضیه کاستیلیانو- محاسبه تغییر شکل از طریق قضیه کاستیلیانو

چهاردهم

ستونها- مقدمه و پایداری سازه ها- فرمول اویلر برای ستونهای دو سر لولا

پانزدهم

تعمیم فرمول اویلر برای ستونهای که تکیه گاه به غیر از تکیه گاه لولایی دارند

شانزدهم

مطالب درسی تدریسی

هفته

The Continuum Concept, Continuum Mechanics, Scalars, Vectors, and Cartesian Tensors, Tensor Algebra in Symbolic Notation —Summation Convention

اول

Indicial Notation, Matrices and Determinants, Transformations of Cartesian Tensors

دوم

Principal Values and Principal Directions of Symmetric Second-Order Tensors

سوم

Tensor Fields, Tensor Calculus

چهارم

Integral Theorems of Gauss and Stokes

پنجم

Stress Principles, Body and Surface Forces, Mass Density, Cauchy Stress Principle, The Stress Tensor

ششم

Force and Moment Equilibrium, Stress Tensor Symmetry, Stress Transformation Laws

هفتم

Principal Stresses, Principal Stress Directions, Maximum and Minimum Stress Values, Mohr’s Circles For Stress

هشتم

Plane Stress, Deviator and Spherical Stress States, Octahedral Shear Stress

نهم

Kinematics of Deformation and Motion, Particles, Configurations, Deformation, and Motion, Material and Spatial Coordinates

دهم

Lagrangian and Eulerian Descriptions, The Displacement Field, The Material Derivative

یازدهم

Deformation Gradients, Finite Strain Tensors, Infinitesimal Deformation Theory, Stretch Ratios

دوازدهم

Rotation Tensor, Stretch Tensors, Velocity Gradient, Rate of Deformation, Vorticity, Material Derivative of Line Elements, Areas, Volumes

سیزدهم

Fundamental Laws and Equations, Balance Laws, Field Equations, Constitutive Equations, Material Derivatives of Line, Surface, and Volume Integrals, Conservation of Mass, Continuity Equation, Linear Momentum Principle, Equations of Motion

چهاردهم

The Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion, Moment of Momentum (Angular Momentum) Principle, Law of Conservation of Energy, The Energy Equation

پانزدهم

Linear Elasticity, Elasticity, Hooke’s Law, Strain Energy, Hooke’s Law for Isotropic Media, Elastic Constants,  Elastic Symmetry; Hooke’s Law for Anisotropic Media,  Isotropic Elastostatics and Elastodynamics, Superposition Principle, Plane Elasticity
 

شانزدهم

مطالب درسی تدریسی

هفته

The Finite element Methods, 2.1) Introduction, Nodes, equilibrium, and continuity, Degrees of freedom, Stiffness equations, Element stiffness equations, Global stiffness equations, Global and local Axes

اول

System restrains: Boundary conditions, Essential boundary conditions, Natural boundary conditions, Mixed boundary conditions, Restraint sufficiency, Steps in finite element process

دوم

Finite stiffness equations by direct methods, Direct determination of element stiffness equations, Element stiffness matrix: Global axes, Element stiffness matrix: Local axes, Element  load vector

سوم

Transformation of element stiffness equations : 1D elements in 2D and 3D spaces, Displacement transformation, Force and moment transformation, Element stiffness matrix transformation

چهارم

Global stiffness equations, Introduction, Assembly of global stiffness matrix, Equilibrium and compatibility at nodes, A process for the assembly, Assembly of global load vector, Applied loads, Support reactions, Global displacement vector

پنجم

Element stiffness equation by displaced state virtual work application, Displaced state of the structure, Global displacement basis functions, Element displacement shape function

ششم

Virtual work basis of element stiffness equations, Principle of virtual work, Element stiffness equations, Beam finite element on an elastic foundation, Axial finite element

هفتم

General Approach to Element Stiffness Equations, Introduction, Stress and strain, Strain and stress displacement relationships, Element stiffness equations

هشتم

Virtual strain displacement relationships, Virtual strain energy, Virtual work of external actions, General expression for element stiffness equations

نهم

Plane stress structural triangular finite element, Introductions, Constant strain triangular element (3-node, 6-dof), Shape and displacement functions, Element stiffness matrix, Load between nodes

دهم

Natural coordinates and quadrature for triangle elements, Natural coordinates for triangular elements, Quadrature for triangle elements, Example of body force

یازدهم

Natural coordinates and quadrature for line segments, Natural coordinates for lines, Quadrature for line segments, Examples of line load, Linear strain triangular element (6-node 12-dof),  Shape and displacement functions, Element stiffness matrix, Numerical quadrature over a triangular area, Load between nodes

دوازدهم

Isoparametric plane stress structural quadrilateral  finite elements, Introduction, Bilinear rectangular element (4 node 8 dof), Shape and displacement functions, Element stiffness matrix

سیزدهم

Quadrilateral element (4-node 8  dof), Isoparametric transformation, Element stiffness matrix

چهاردهم

Quadrature rules, Nodal point quadratures,  Gaussian quadrature: function of one variable, Gaussian quadrature: function of two variables

پانزدهم

Element mapping and master element calculations, Element mapping, Master element stiffness calculations, Master element equallent nodal loads, Quadratic quadrilateral elements, Serendipity elements (8 node 16 dof), Lagrange elements (9 node 18 dof)

شانزدهم

مطالب درسی تدریسی

هفته

Fracture of Cracked Membersو

PRELIMINARY DISCUSSION, Cracks as Stress Raisers , Behavior at Crack Tips in Real Materials , Effects of Cracks on Strength ,Effects of Cracks on Brittle Versus Ductile Behavior , Internally Flawed Material

اول

Mathematical concepts, Strain Energy Release Rate, G, Stress Intensity Factor, K, Additional Comments on K and G

دوم

APPLICATION OF K TO DESIGN AND ANALYSIS, Mathematical Forms Used to Express K
  Discussion, Cases of special interest for practical application, Superposition for combined loading

سوم

Fracture toughness and values and trends, Trends in fracture toughness  with materials,  Effects of temperature and loading rate, Microstructure influence on fracture toughness, Mixed mode fracture mechanics

چهارم

plastic zone size, and plasticity limitation on LEFM, Plastic zone size for plane stress, Plastic zone size for plane strain, Plasticity limitation on LEFM, Plane stress versus plane strain

پنجم

Discussion of fracture toughness testing, Standard test methods,  Effect of thickness on fracture behavior, Use of plane stress fracture data

ششم

INTRODUCTION, DEFINITIONS AND CONCEPTS, Description of Cyclic Loading , Point Stresses 9.1 INTRODUCTION, DEFINITIONS AND CONCEPTS, Description of Cyclic Loading , Point Stresses Versus Nominal Stresses, Stress Versus Life (S-N) Curves  Versus Nominal Stresses, Stress Versus Life (S-N) Curves

THE PHYSICAL NATURE OF FATIGUE DAMAGE, TRENDS IN S-N CURVES, Trends with Ultimate Strength, Mean Stress, and Geometry, Effects of Environment and Frequency of Cycling , Effects of Microstructure, Residual Stress and Other Surface Effects , Statistical Scatter

هفتم

MEAN STRESSES, Presentation of Mean Stress Data, Normalized Amplitude-Mean Diagrams, Life Estimates with Mean Stress, MULTIAXIAL STRESSES, One Approach to Multiaxial Fatigue, Discussion, VARIABLE AMPLITUDE LOADING, The Palmgren–Miner Rule, Cycle Counting for Irregular Histories

هشتم

Notch effect, The fatigue notch factor  kf and causes of kf < kt, Notch sensitivity and empirical estimate of kf, Notch effect at intermediate and short lives

نهم

10.5) Combined effects of notches and mean stress,  Brittle material , Ductile material

   Discussion

دهم

Estimating long fatigue strength (fatigue limit), Estimating of smooth specimen fatigue limit, Factors affecting long-life fatigue strength, Reduction factor for fatigue limit

یازدهم

Estimating S-N curves,  Estimating by the method of Collins, Estimating by the method of Juvinall or Shigley

دوازدهم

Design to avoid fatigue failure, Design details, Surface residual stress,  Variable amplitude loading

   Safety factor

سیزدهم

Preliminary discussion, Need for crack growth Analysis, Definitions for fatigue crack growth, Describing fatigue crack growth behavior of materials, Fatigue crack growth rate testing , Test methods and data analysis, Test variables, Geometry independent of da/dN vs. ∆K curves

چهاردهم

Effects of R=Smin/Smax on fatigue crack growth, Effects on ∆Kth, The Walker equation, The Forman equation, Other equations

پانزدهم

Trends in fatigue crack growth behavior, Trends with material, Trends with temperature and environment, Life estimate for constant amplitude loading, Closed form solution

شانزدهم