Structures Engineering Courses

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Finite Element Analysis (FEA) — Heat Conduction and Mass Diffusion at Steady-State

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Finite Element Analysis (FEA) — Linear and Elliptic Partial Differential Equations for a Scalar Variable in Two Dimensions

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Finite Element Analysis (FEA) — Boundary Conditions, Basis Functions, and Numerics

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Finite Element Analysis (FEA) — The Matrix-vector Form

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Finite Element Analysis (FEA) — Variational Principles

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Finite Element Analysis (FEA) — Analysis of the Finite Element Method

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Finite Element Analysis (FEA) — Lagrange Basis Functions and Numerical Quadrature in 1D Through 3D

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Finite Element Analysis (FEA) — The Finite-dimensional Weak Form

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Harmonic Response Analysis in Ansys Mechanical

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Single-Point Response Spectrum Analysis Using Ansys Mechanical

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Mode Superposition Transient Analysis

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Topology Optimization Using Ansys Mechanical

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Volumetric and Deviatoric Behavior

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This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

In this course, we will discuss the strong form of steady-state heat conduction and mass diffusion. We will introduce the Fourier Law of heat conduction and temperature and heat flux will be discussed. The boundary conditions like concentration and mass influx with respect to mass diffusion. Then we will derive an equivalent infinite-dimensional weak form from the strong form of steady-state heat conduction and mass diffusion. After that, an equivalent finite-dimensional weak form is derived from the infinite-dimensional weak form. Further, we also discuss a general eight-node brick element or hexahedral element and the trilinear basis functions used in its formulation. In the following lessons, we will talk about the Jacobian of the map, followed by the integrals in terms of the degree of freedom of an element. Lastly, we will conclude with the matrix-vector weak form.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we will discuss how to solve linear, hyperbolic partial differential equations for an unknown vector in three dimensions and apply the findings to study linear elastodynamics. The problem is time-dependent and so are the boundary conditions. Apart from boundary conditions, we also need initial conditions to solve this class of problems. We discuss various time discretization methods and the Newmark family of algorithms used to solve time-dependent problems. We then write the time-discretized problem in its modal form and learn how to solve it. We end the course with a discussion about the stability analysis and amplification matrix for such problems.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course discusses the process of building two-dimensional problems for the linear and elliptic PDEs using a scalar variable. The strong and the weak form are discussed using constitutive relations and boundary conditions. Then, it talks about the gradient of the trial solution and the weighting function. Lastly, it discussed the matrix-vector weak form.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course focuses on obtaining the weak form using Variational Methods. Further, it discusses potential energy or Gibbs Free Energy. We will talk about ‘Pi’ as free energy functional and how the extrema can be used to check equilibrium states. Next, we discuss the variation in ‘Pi’ with respect to the variation in the field. Then, we will see how the extremization of free energy functional is performed.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

In this course, we derive the matrix-vector weak form which is used in the finite element method. We begin by deriving the matrix-vector form for a single general element and then proceed to derive it for the entire problem domain by assembling the matrix-vector forms for all the elements in the domain.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course focuses on obtaining the weak form using Variational Methods. Further, it discusses potential energy or Gibbs Free Energy. We will talk about ‘Pi’ as free energy functional and how the extrema can be used to check equilibrium states. Next, we discuss the variation in ‘Pi’ with respect to the variation in the field. Then, we will see how the extremization of free energy functional is performed.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.

This course discusses why and how the FEA works and what are the special properties of the FEA. The norms that represent the finite-dimensional trial solution will be discussed. The important properties of the finite element method – consistency and the best approximation - will be explained in detail. Later, we will discuss the Pythagorean Theorem. The Sobolev estimates and convergence of the FEM will be explained further. And lastly, we will talk about finite element error estimation.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we will discuss the use of Lagrange Polynomials in the basis functions in 1 through 3 dimensions. The formula for the basis functions is first written in 2D and then in 3D. We will further talk about the Gaussian Quadrature for numerical integration. Lastly, triangular and tetrahedral elements are discussed using these basis functions.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. In this course, we begin by discussing linear elliptic partial differential equations (PDEs) in one dimension. We discuss various elements required for solving PDEs, such as the boundary conditions and the constitutive relations. We then discuss the strong and weak forms of the PDEs and show how the two forms are equivalent.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.
In this course, we discuss how the infinite-dimensional weak form of a 1D linear elliptic PDE can be transformed to a finite-dimensional weak form which forms the basis of the finite element method. We discuss basic Hilbert spaces, which are functional spaces in which acceptable solutions to the weak form exist. We also discuss basis functions and how the finite-dimensional weak form can be written as a sum over the finite subdomains (or elements) of the problem.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys.
In this course, we will discuss how to solve linear, hyperbolic partial differential equations for an unknown vector in three dimensions and apply the findings to study linear elastodynamics. The problem is time-dependent and so are the boundary conditions. Apart from boundary conditions, we also need initial conditions to solve this class of problems. We discuss various time discretization methods and the Newmark family of algorithms used to solve time-dependent problems. We then write the time-discretized problem in its modal form and learn how to solve it. We end the course with a discussion about the stability analysis and amplification matrix for such problems.

This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert, at the University of Michigan in partnership with Ansys. This course focuses on parabolic problems. The problems that will be discussed are linear parabolic PDEs in three dimensions for a scalar variable. Physical problems such as unsteady heat conduction and unsteady mass diffusion are considered here.

 

 

 

Topology optimization is the numerical technique used to obtain the optimal layout of structural components by determining the areas of the parts which can be removed to maximize stiffness while reducing weight and keeping maximum stress below a certain value. This method is becoming more popular due to improvements made in additive manufacturing and 3D printing process. It is now much easier to produce parts having complex and organic looking shapes coming out from topology optimization. Reducing weight is a critical factor for student teams to maximize vehicle performance. While performing stress analysis, there are areas in the product which doesn’t show any values of stress under loading conditions. The optimization technique identifies the low-stress areas and clears them according to the various criteria set by the user and delivers a less weighted product. In this course, you will learn how to carry out topology optimization using Ansys Mechanical.

 

Ansys Sherlock is the only reliability physics-based electronics design tool that provides fast and accurate life predictions of electronic hardware at the component, board and system levels in early-stage design. With embedded libraries containing over 200,000 parts, Sherlock rapidly converts electronic computer-aided design (ECAD) files into computational fluid dynamics (CFD) and finite element analysis (FEA) models.
Ansys Sherlock is the cornerstone of our Electronics Reliability solution. Start here to learn more about our reliability prediction tool.

A current passing through a metal heats it up in what is commonly called Ohmic heating. In this phenomenon, the metal heats up because of the electrical resistance offered by the metal to the flowing current. As this heating continues, the temperature of the metal becomes uniform throughout and continues to rise with time. The temperature rise can weaken the metal or even deform in to an extent that it may become structurally fragile. Using the finite element method, it is possible to estimate the time it takes for the body to reach a certain temperature.In this SimCafe course, we will highlight the step-by-step procedure to perform the thermal analysis across the platinum micrometer bridge circuit using Ansys Thermal

The trachea, commonly known as the windpipe, is a cartilage tube that connects the larynx, which is an organ in the neck, to the bronchi tubes in the lungs. With each inhalation, the trachea widens and elongates. Similarly, as we exhale, it returns to its resting position. During the respiration process, the air moving in and out of our lungs exerts forces on the inner walls of the trachea. In this SimCafe Course, we will learn to simulate the effect of air pressure on the trachea using Ansys Mechanical.

Generally, the solution in Ansys Mechanical is calculated in a cartesian coordinate system. In case of a curved structure, such as curved beams and pressure vessels, it is more intuitive to visualize the results in the axial, radial, and circumferential directions. In this course, we will use a solved model of a curved beam with a rectangular cross-section under a moment and learn to post-process the results in the cylindrical coordinate system. In this SimCafe course, we will outline the detailed steps to post-process as well as discuss how to interpret the results using Ansys Mechanical.

When designing the structure, it is important to take the gravitational force into account. Even in the absence of external operating loads, the weight of the structure is always acting on the body and is trying to pull the structure towards the earth. In this SimCafe course, we will learn about simulating stresses developed due to the Earth’s gravity on a canonical structural component using Ansys Workbench.

Contacts are essential means of transferring forces in any mechanical system. Although the mechanical components are designed to sustain the operating forces, special care must be taken for the contacts as they are found in very small areas. Because of this, the transferred loads through such small areas develop high stresses. These localized stresses may result in highly localized yielding. In this Sim Café course, we we will learn to solve the contact mechanics on a simple spherical canonical object that is in contact with a rigid wall using Ansys Mechanical.

ModelA signpost is an example of a combined loaded structure, a structure which experiences both axial and bending loads. The weight of the signboard acting through its center of gravity (CG) creates a bending moment that results in bending stresses. The weight of the signpost acting along the axis of the column structure creates additional compressive stresses in the column. Finally, we also must consider environmental factors such as the pressure loading due to the blowing wind. In this Sim Café course, we demonstrate the structural analysis of a 3D Signpost structure using step-by-step instructions in Ansys Mechanical.

A bike crank is a lever arm that gives the bicycle rider a mechanical advantage when pedaling. When the rider presses their feet on the pedals, the bike crank revolves and causes rotation of the sprocket wheel. This drives the chain, which in turn drives the rear wheel​. In this SimCafe Course, we will learn how to simulate mechanical crank part to analyze the strain using Ansys Mechanical and compare the strain values with the analytical approach.

Beams are one of the most used fundamental structural elements. The deflection and load-carrying characteristics can be obtained using the beam theory formulation. In this course, we simulate the load-carrying capacity of a simple cantilever beam using beam elements. We will also estimate the modal frequencies using beam theory. On comparing the obtained results, we find that the Ansys beam element results match closely with the beam theory. In this SimCafe Course, we will learn a detailed setup of the modal analysis of a Cantilever structure using beam elements in Ansys WorkBench.

The structures are subjected to various loading. The objective of the design engineer is to ensure that the structure has minimum stresses and strains. Using the Ansys optimization tools, engineers can solve structural optimization problems. The optimised designs is where multiple input parameters can control and optimize the design objectives. In this SimCafe Course, we provide a detailed walkthrough of the Optimization analysis of a structural problem in Ansys Workbench.

Almost all bodies undergo thermal expansion i.e., their volume increases as the temperature of the body is increased. If the body is constrained, it cannot freely expand with increasing temperatures and the object of interest develops stresses, which are often called thermal stresses, because of this confinement. Mechanical components are generally constrained to achieve the desired mechanism. Hence, these components can generally develop thermal stresses in high-temperature environments. In this SimCafe course, we will look at a canonical problem involving a bar that is rigidly fixed at one end and estimate the thermal stresses in this bar using Ansys Workbench.

Excessive vibration of the wing can cause a catastrophic failure that, more often than not, leads to loss of life or property. When designing any system, it is important to have a sound knowledge of its naturally excited vibration frequency. To avoid resonance, it is important to design the wing such that the natural frequency of the wing does not match the external frequencies of vibrations. In this SimCafe Course, we will learn to perform the modal analysis of a wing and estimate the first 6 modes of vibration in Ansys Workbench.

Modeling the beams using 3D elements increases the overall solver time compared to the simplified 1D approximation. Having said that, you might wonder — is it possible to model the beams using 2D elements? If so, which of the following approximations is more appropriate — plane stress or plane strain? And finally, how much is accuracy compromised by this assumption? This course provides the answers to all of the above questions. In this Sim Café course, we demonstrate the structural analysis of a simply supported beam using a 2D approximation in Ansys Mechanical.

In this course, balance laws will be discussed, including the balance of mass, momentum, and energy. The balance of mass can be associated with diffusion. The balance of linear momentum is associated with Newton’s laws of motion, and the balance of angular momentum is associated with Euler’s equation. The balance of energy gives rise to the heat equation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

We have learned that constitutive laws/relations are important for the study of continuum mechanics. In this course, the focus will be on how the behavior of a material can be captured by using constitutive relations. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we discuss the frame of reference and material symmetry and how it affects the constitutive relations. We also discuss the objectivity of several classes of materials such as elastic, hyperelastic solids, and viscous fluids. We also briefly discuss Navier Stokes equations which is an initial and boundary value problem in fluid mechanics.

In this session, the balance of mechanical energy will be explored along with differing measures of stress.  We will then delve into the work conjugate relations. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we will begin by discussing the two laws of thermodynamics — the balance of energy law and the entropy inequality law. We then use the Legendre transformation to derive the Helmholtz free energy. Following this, we discuss the Clausius-Planck and the Clausius-Duhem inequalities. We then study thermoelasticity, which explains how a body stores internal energy as it deforms due to local temperature changes. Finally, we conclude this course by discussing the heat flux vector in current and reference configurations. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we begin by discussing what variational principles are and how they can be applied to nonlinear elasticity. We then apply variational derivatives for nonlinear elasticity to develop the weak form of balance of linear momentum for static problems. Finally, we use integration by parts to transform this weak form into the strong form of nonlinear elasticity. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

This short course is intended to discuss the solution for boundary value problems. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we will discuss mass transport by considering the transport of the substance through space. Next, we will talk about the constitutive relations for flux in mass transport. Then, we will set up the foundation for the treatment of mass transport in continuum physics. Lastly, we will discuss the role of interfacial free energy and the Cahn-Hilliard formulation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we will talk about deriving linearized elasticity. This can be explained using kinematics, constitutive relations, and the balance of linear momentum. As we conclude our learning on the continuum mechanics, we will do a quick recap followed by giving due credits and discussing different books for this subject.

This course discusses the mathematical quantities called tensors and, their properties. Tensors and vector fields are discussed as well.
This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we discuss how to mathematically describe the distortion that solids and fluids undergo. We cover important topics such as (i) deformation of curves, surfaces and volumes; (ii) measures of strain; (iii) polar decomposition and (iv) rate of deformation. On completing this course, we will have a better understanding of the kinematics that underlies continuum mechanics. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

This course starts with a discussion on the motion of continuum bodies — how to describe and analyze the motion. The lectures cover the study of kinematics of motion divided into four subcategories: Motion and Deformation, Lagrangian description, Eulerian description, and Material Derivatives. From basic representation, all the subcategories will be discussed in this course. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we first discuss what exactly continuum physics means. Then we revisit vectors and revise concepts such as basic operations of vectors, basis vectors, etc.
This course was created for Ansys Innovation Courses by Professor Kresihna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

When designing any system, it is important to have a sound knowledge of its naturally excited vibration frequency. If the structure experiences an external vibration in the range of its natural frequency, it creates resonance. This can cause a catastrophic failure of the system. In this SimCafe course, you will learn the end-to-end workflow for importing a realistic geometry and understand the importance of performing modal analysis of a space satellite. You will set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using step-by-step instructions.

A body at any temperature can exchange energy with its surroundings in the form of thermal radiation, which is characterized by the emission of electromagnetic waves from the body. It is the only mode of heat transfer that does not require a medium and can take place in a vacuum. Therefore, in space applications, it becomes important to understand the amount of heat incident on the systems. In this Simcafe Course we show how to analyze and estimate the net thermal radiation of a system under realistic boundary conditions using Ansys Transient Thermal.

When designing any system, it is important to have a sound knowledge of its naturally excited vibration frequency. If the structure experiences an external vibration in the range of its natural frequency, it creates resonance. This can cause a catastrophic failure of the system. In this SimCafe course, you will learn the end-to-end workflow for importing a realistic geometry and understand the importance of performing modal analysis of a space satellite. You will set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using step-by-step instructions.

During the heat transfer process, the temperature of the body is either increasing or decreasing with time. Any change in the imposed thermal conditions of the body, such as the addition of a heat source or sink or change in the boundary condition, will cause the system to undergo a transient approach for establishing a different steady-state solution. In this SimCafe course, we show how to simulate and analyze the transient heat conduction of a system under realistic boundary conditions using Ansys Transient Thermal.

FEA simulations are used to study the mechanical behavior of bone tissues. The real-life bone tissue model is obtained from CT scans. Multiple CT scans are merged together to create a 3D bone model. Bones/skeletons bear the structural loads that bodies encounter; failing to do so can cause a fracture. In this SimCafe course, you will learn to estimate the equivalent stiffness of the 3D bone structure in Ansys WorkBench using Ansys Mechanical. You will set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using step-by-step instructions.

Buckling analysis calculates the buckling load factor and associated mode shapes. The buckling load factor multiplied by the applied load gives the magnitude of the compressive load that can cause buckling. In this SimCafe course, you will learn to analyze buckling on a simple column by following the end-to-end workflow in Ansys Structural. You will create the computational mesh and set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using immersive step-by-step walk-through videos.

The design of the telescope truss should be able to sustain dynamic loads and must be flexible enough to provide support for different motions. In this SimCafe course, you will learn end-to-end workflow for importing a realistic geometry and understand the importance of FEA simulations when designing the telescope truss. You will create the computational mesh and set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using step-by-step instructions.

Pressure vessels are used in transportation for storage of gases and liquids. Many gases are stored at very high pressure in the liquid form. The pressure vessels are designed mainly to have high strength in both the circumferential (hoop strength) and axial directions. In this SimCafe Course, we will learn to estimate the hoop, axial, and radial stresses in pressure vessels using Ansys Structural.

Four-point bending strength is performed to analyze the flexural strength of a material. In this SimCafe course, you will learn to conduct this test, virtually, on a simple T-beam, made of structural steel, to understand the boundary condition setup by following the end-to-end workflow in Ansys Structural. You will create the computational mesh and set up the boundary conditions needed for the simulation. The fundamental concepts and the steps needed to successfully model this structural problem are explained using immersive step-by-step walkthrough videos.

Stepped shafts are widely used in drive trains. Mostly supported by bearings at the end, the shaft experiences bending loads, axial thrust, and torsional loads. The shaft must have greater strength to withstand these loads. In this Sim Café course, you will learn to estimate the axial stress concentration on a stepped shaft under axial tension using Ansys Structural.

Evaluation of the structural integrity of assemblies often involves proper modeling and analysis of bolted connections, including the consideration of bolt preload effects. The preload on bolts makes it possible for forces to be transferred between clamped parts effectively, whereas loose bolts may cause failure. Preloaded bolts are also often used in applications with liquids and need to prevent leakage, so bolt preload is a necessary component of such simulations.