![]() Introduction to Finite Element Analysis for Soft and Biological Materials One-week Workshop, Study Abroad Undergraduate Course, Spring Break 2019, Purdue University and Universidad Panamericana Newton's second law, work-energy, impulse-momentum. Particle motion, velocity and acceleration with cartesian, path and polar descriptions. Basic Mechanics II: Dynamics (ME274) Undergraduate Course, Purdue University Stress and strain analyses and elementary failure criteria. Internal reactions resulting from axial, shear, torsional, and bending loading. Free body diagrams, equilibrium of a particle and of rigid bodies. Basic Mechanics I: Statics (ME270) Undergraduate Course, Purdue University Element selection, full or reduced integration, linear or quadratic, mesh convergence, accuracy of displacements and stresses. Steady state and transient heat transfer in 2D. Linear elasticity in 2D (plate with a hole). Trusses by writing directly the input file. Solution of 2D heat transfer with linear triangles and quadrilaterals. Numerical integration in 2D with linear quadrilaterals. Interpolation and plotting with linear triangles and linear quadrilaterals. Solution of 1D linear elasticity and heat transfer with linear and quadratic elements. Linear and quadratic shape functions, interpolation and plotting. Solution of linear elasticity problems with the constant strain triangle. Discretization of displacement field, stress, and strain with finite elements: the Be matrix. ![]() Linear elasticity in 2D, strong form and weak form. Linear quadrilateral element, the isoparametric map in 2D, numerical integration in 2D. Discrete weak form with linear triangular elements and resulting system of equations. Discretization of functions in 2D with linear triangular elements. Strong and weak form of heat transfer in 2D and 3D. Solution of 1D problems with quadratic elements. Discrete weak form and system of equations for linear elements. ![]() Discretization of functions and derivatives in 1D with linear and quadratic shape functions. Strong form and weak form in 1D for linear elasticity and heat transfer. Trusses in one-dimension (1D) and two-dimension (2D) as already discrete systems to introduce the finite element assembly process and solution of the linear system of equations. Additionally, at the time of writing, with the Covid-19 pandemic, some of the lectures are available through the M489 Youtube channel Some of the course materials, in particular the Python labs, are available through our Github. This course has three components: Theory, Python programming labs, Abaqus labs. All the tutorials are completely free.Teaching Introduction to Finite Element Analysis (ME489) Undergraduate Course, Purdue University This website contains more than 200 free tutorials! Every tutorial is accompanied by a YouTube video. This is symbolically illustrated by the following graph. What should be observed is that from the mechanics point of view, the situations in Figs. Under the condition that we add an additional moment of a couple, we can “safely” translate forces from one point to another. So, we have demonstrated the procedure for moving forces from one point to another. Fig 3: the action of the original force F acting at point Q is replaced by the force F acting at point X and a moment of the couple. Now, it should be observed that the original force at the point and the force acting at the point, form a couple whose moment is equal to where is the shortest distance between the two parallel lines passing through and. That is, the two new forces can be canceled, however, we are not going to cancel them. The two forces that are added have to be of opposite signs in order not to disturb the original action of the force. Now, we add two forces whose intensities are equal to the intensity of, and whose action lines are parallel to the action line of the force. The goal is to “move” the force from the point to the point, where can be an arbitrary point. So let us see how this works in practice.Ĭonsider the figure shown below. The main idea is to replace the force, with a force and a moment whose action on the body is equivalent to the action of the original force.Įquivalence of two force systems: Two force systems are equivalent if they result in the identical resultant force and the identical resulting moment. ![]() Basically, to make a long story short, a force acting at a certain point can be moved (without rotating the line of action of the force) to an arbitrary chosen point X if a couple is added whose moment is equal to the moment of the force around point X (X is the symbol for the point).
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