Introduction to Solid Mechanics

Solids

A body is and remains continuous under the action of external force. That means:

• Consist of continuous material points.
• Can sustain shear.
• Neighboring points remains neighbors.

Solid Mechanics

We will discuss what steps are taken out to understand the dynamic or static response of structure. Steps are:

• Computation or Modelling 
• Finite element method 
• Boundary element method
• Molecular dynamics simulation

• Theory or Analytical Modelling
• Continuum mechanics
• Micromechanics 
• Constitutive model

• Experiments 
• Material characterization
• Strain measurement 
• High strain rate
• Fatigue

Defining a Problem

1. Describe the goal and desired information.
2. Model the geometry of solid.
3. Determine the loading applied to the solid.
4. Describe what modelling must be included in the model.
5. Choose a constitutive law which describe the behavior of material.
6. Choose a method of analysis.
7. Solve the problem.

While defining a problem, we need t consider failure mechanisms as under:

• Critical loads to cause fracture in a brittle or ductile solid containing a crack.
• Fatigue life of a component under cyclic loading.
• Rate of growth of a stress-corrosion crack in a component.
• Creep life of a component.
• Finding length of crack that a component can contain and still withstand fatigue or fracture.
• Wear rate of a surface under contact loading (like gears).
• The fretting or contact fatigue life of a surface.

Types of Loads Acting on Machine Element

Types of loads are described below:

1. Steady or Dead Load  ↔  load do not change with time and no shift of elements from original position.
2. Variable or Live Load  ↔  if load changes continuously with time.
3. Shock Load  ↔  if load is suddenly applied or removed.
4. Impact Load  ↔  when load is applied from a certain height or distance (its intensity increases).

Steps for Finding which Structure is Best?

First you have to do Hand Calculations and the steps are:

1. Draw structure 
2. Find External support reactions
3. Solve for Internal reactions at specified location.
4. Find if internal reactions (normal stress, shear stress, bending stress) cause different stress distributions.
5. Geometric analysis of cross-section of the member 
6. Define state of stress at different locations (3D with Z-axis ↔ General State of Stress, 2D with Z-axis ↔ Planar State of Stress)
7. Stress Transformation  ↔  rotation of 2D body changing its Planar Stress State
8. Quantify the deformation of material (deformation can be size change, shape change, elastic curve)
9. Design of Simple mechanical structure

Now, its time for Analytical Solution (mostly ANSYS) and the steps are:

1. Draw body structure
2. Define its Material
3. Meshing depending upon the surface 
4. Boundary conditions 
5. Solution results

Once solution for analytical method carried out, we compare both solutions (by Hand or by Ansys), we use experimental method to take out further results and then draw conclusion that structure is capable of holding that load or not.

Surface structure is made from a material having small thickness compared to its other dimensions. Structures are classified as:

• Angle sections
• C Channel Rod
• I-section beams
• Holland Profile

3'S Concepts

We are here to design and produce a variety of objects and structure. A safe and successful design must adhere following mechanical concerns:

1. Strength  ↔  object is strong enough to withstand load applied and repeated loadings.
2. Stiffness  ↔  object deflect or deform so much that it cannot perform its intended function.
3. Stability  ↔  object suddenly bend or buckle out of shape at some elevated load.

Structural Design

Design loading is specified in codes (requirement for the actual structural design). For E.g.: dead loads, live loads, snow loads, wind loads, seismic loads, hydrostatic and soil pressure.

• Considerations of material and load uncertainties are very important.

Allowable Stress Design (ASD) 

• A single factor of safety which include material and load uncertainties. 
• Computed Elastic Stress should not exceed Allowable Stress for each load combinations.

For ASCE 7-10 standard include:

• Dead load
• (0.6) dead load + (0.6) wind load
• (0.6) dead load + (0.7) earthquake load

Load & Resistance Factor Design (LRFD)

There has been an increasing trend to separate material uncertainty from load uncertainty called Strength Design or LRFD.

For ASCE 7-10 standard include:

• (1.4) Dead load
• (0.9) dead load + (1.0) wind load
• (0.9) dead load + (1.0) earthquake load
• (1.2) dead load + (1.6) live load + (0.5) snow load

Note:

• Aerospace Structure and Materials
• Civil Engineering Projects
• Carbon Nanotubes
• Composite Materials
• Aerospace Composites - Carbon fiber, Glass fiber, Kevlar, Thermoplastic composites

References:

• Material from Class Lectures + Book named Engineering Mechanics of Materials by R.C. Hibbeler (6/9th Edition) + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube (Engineering Sights).