Key Concepts in Finite Element Method (FEM) Analysis
Fundamental Concepts in Finite Element Method (FEM)
Sources of Nonlinearity:
- Constitutive relations (material)
- Changes of geometry (strain, displacements)
- Boundary Conditions (contact)
- Loads (deformation)
Why FEM is Important:
- It replaces a continuous structure with a model having a finite number of points.
- It describes physical phenomena for which analytical solutions are not known.
Nonlinear Elastic Materials:
Present nonlinear stress-strain relationships even at infinitesimal strains.
Linear Elastic Materials:
Read MoreTheodolite Components, Functions, and Measurement Principles
Theodolite: Essential Surveying Instrument
A theodolite is an instrument for universal mechanical-optical measurement used to measure vertical and horizontal angles with great precision.
Key Components of a Theodolite
- Base: A leveling base equipped with leveling screws, a circular level, and a spherical plumb.
- Levels:
- Annular (O-ring) Levels: The bubble is coincident with the center of the tube.
- Spherical Levels: The bubble is coincident with the inner circle.
- Plumb: Used to ensure the theodolite is vertically
Structural Engineering Concepts: Supports, Stress, Vibration
Types of Structural Supports
1. Pinned Support
A pinned support, also known as a hinge support, allows rotation but restricts translational movement in any direction.
Characteristics:
- Resists horizontal and vertical forces
- Allows rotation
- Commonly represented in diagrams as a triangle or a hinge symbol
Applications:
- Trusses: Pinned supports are often used in truss structures, such as bridges, to allow for some degree of rotation while ensuring stability.
- Beams: In structural frames, pinned supports provide
Structural Mechanics: Key Concepts and Definitions
Isotropic: An isotropic material behaves the same in all directions.
Anisotropic: Direction-dependent materials are anisotropic – not isotropic.
Bearing Stress: Internal stress caused by compressive forces (contact pressure between separate bodies).
Center of Mass: The point at which there is equal mass in all directions.
Centroid: The point at which there is equal volume on all sides, first moment area (ydA).
Characteristics of a Force: Location/point of application (dimensions), magnitude (units),
Read MoreUnderstanding Architectural Floor Plans and Key Terms
Understanding Architectural Floor Plans
In architecture and building engineering, a floor plan is a technical drawing to scale, showing a view from above of the relationships between rooms, spaces, and other physical features at one level of a structure. Dimensions are usually drawn between walls to specify room sizes and wall lengths. Floor plans may also include details of fixtures such as sinks, water heaters, furnaces, and similar items. They can incorporate notes for construction specifying
Read MoreMechanics of Materials: Stress, Strain, and Torsion
Chapter 1-4 Summary
Chapter 1: Friction and Belts
FBD (Free Body Diagrams) are starters for all questions!
For friction, Fr = μ x N, where three surface conditions exist: smooth dry, rough dry, and lubricated surfaces.
For friction between coaxial discs, let the friction on an infinitesimal element of area be δF = (2π x δr)p x μ. The frictional torque on the element of area is δT = r x δF. For the whole disc:
T = 2πμ∫r1r2 r2 p dr, where p varies with r.
Case 1: If p is constant, then T = (2π/
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