Finite Element Method and Computational Structural Dynamics | EveryEng

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Finite Element Method and Computational Structural Dynamics

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1800 min

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Why enroll

This course is ideal for postgraduate students, structural engineers, researchers, and analysts who want to master advanced numerical methods for structural analysis. As modern structures become more complex and performance-based design gains importance, computational structural dynamics has become essential for safe and efficient design.

Enrolling in this course helps learners:

Gain strong foundations in finite element formulation
Develop expertise in dynamic analysis of structures
Understand nonlinear and time-dependent structural behavior
Improve skills in numerical modeling and simulation
Prepare for careers in structural design, research, and advanced analysis

The course is especially valuable for professionals involved in earthquake engineering, vibration analysis, high-rise structures, bridges, and performance-based design.

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Is this course for you?

You should take this if

You work in Infrastructure & Construction
You're a Civil & Structural / CAD & Analysis professional
You have 3+ years of hands-on experience in this field
You prefer self-paced learning you can revisit

You should skip if

You're new to this field with no prior experience
You need a different specialisation outside Civil & Structural
You need live interaction with an instructor

Course details

The Finite Element Method and Computational Structural Dynamics course provides advanced knowledge of numerical techniques used to analyze structural behavior under static and dynamic loading conditions. The course integrates finite element formulation with computational approaches to study structural response to time-dependent loads such as earthquakes, wind, impact, and machine-induced vibrations.

The course begins with a detailed review of finite element fundamentals, including discretization, interpolation functions, element formulation, and assembly procedures. Learners then explore structural dynamics concepts, such as degrees of freedom, mass and stiffness matrices, damping models, and equations of motion. Various time-integration and frequency-domain solution techniques are discussed to simulate dynamic response accurately.

Advanced topics include nonlinear structural dynamics, geometric and material nonlinearities, stability and buckling analysis, and response of structures under seismic excitation. The course emphasizes computational implementation, numerical stability, convergence, and result interpretation. Practical applications in buildings, bridges, aerospace, and mechanical structures are incorporated to connect theory with real-world engineering problems.

By the end of the course, learners develop the ability to model, analyze, and interpret complex structural systems using FEM-based computational tools.

SOURCE- Youtube [NPTEL IIT Roorkee]

Course suitable for

Key topics covered

Fundamentals of finite element method (FEM)
Discretization and interpolation functions
Element stiffness and mass matrix formulation
Assembly and boundary conditions
Governing equations of structural dynamics
Single and multi-degree-of-freedom systems
Free and forced vibration analysis
Damping models and energy dissipation
Modal analysis and mode superposition
Time integration methods (Newmark, Wilson, central difference)
Frequency-domain and response spectrum analysis
Nonlinear structural dynamics
Geometric and material nonlinearities
Stability, buckling, and post-buckling analysis
Seismic response of structures
Numerical stability, convergence, and error control
Computational implementation and result interpretation

Course content

The course is readily available, allowing learners to start and complete it at their own pace.

60 lectures30 hr

Lecture 01 Introduction to Scientific Computations I
31 min
Lecture 02 Introduction to Scientific Computations II
29 min
Lecture 03 Basic Concepts of Linear Algebra
24 min
Lecture 04 Polynomial Interpolation and Numerical Quadrature I
33 min
Lecture 05 Polynomial Interpolation and Numerical Quadrature II
33 min
Lecture 06 Polynomial Interpolation and Numerical Quadrature-III
31 min
Lecture 07 Polynomial Interpolation and Numerical Quadrature IV
24 min
Lecture 08 Mathematical Modelling and Approximate Solutions I
30 min
Lecture 09 Mathematical Modelling and Approximate Solutions II
26 min
Lecture 10 Mathematical Modelling and Approximate Solutions III
31 min
Lecture 11 Approximation via Variational Principles
28 min
Lecture 12 Introduction to the Finite Element Concept
26 min
Lecture 13 Finite Elements of C^0 Continuity in 1-D- I
31 min
Lecture 14 Finite Elements of C^0 Continuity in 1-D - II
27 min
Lecture 15 Finite Elements of C^0 Continuity in 1-D - III
36 min
Lecture 16 Finite Elements of C^0 Continuity in 1 D IV
28 min
Lecture 17 Finite Elements of C^1 Continuity in 1 D I
25 min
Lecture 18 Finite Elements of C^1 Continuity in 1 D II
30 min
Lecture 19 Finite Elements of C^0 Continuity in 2 D & 3 D I
26 min
Lecture 20 Finite Elements of C^0 Continuity in 2 D & 3 D II
28 min
Lecture 21 Finite Elements of C^0 Continuity in 2 D & 3 D III
32 min
Lecture 22 Finite Elements of C^0 Continuity in 2 D & 3 D IV
27 min
Lecture 23 Finite Elements of C^0 Continuity in 2 D & 3 D V
24 min
Lecture 24 Finite Elements of C^0 Continuity in 2 D & 3 D VI
28 min
Lecture 25 Finite Elements of C^0 Continuity in 2 D & 3 D VII
28 min
Lecture 26 Finite Elements of C^0 Continuity in 2 D & 3 D VIII
21 min
Lecture 27 Finite Elements of C^0 Continuity in 2 D & 3 D IX
33 min
Lecture 28 Finite Elements of C^0 Continuity in 2 D & 3 D X
40 min
Lecture 29 Finite Elements of C^0 Continuity in 2 D & 3 D XI
30 min
Lecture 30 Finite Elements of C^0 Continuity in 2 D & 3 D XII
41 min
Lecture 31 Mapped Elements I
32 min
Lecture 32 Mapped Elements – II
33 min
Lecture 33 Mapped Elements – III
37 min
Lecture 34 Mapped Elements – IV
30 min
Lecture 35 Mapped Elements – V
30 min
Lecture 36 Variational Crimes
34 min
Lecture 37 The Patch Test
28 min
Lecture 38 Finite Elements for Plates and Shells – I
27 min
Lecture 39 Finite Elements for Plates and Shells – II
30 min
Lecture 40 Finite Elements for Plates and Shells – III
37 min
Lecture 41 The Time Dimension and Dynamic Effects I
32 min
Lecture 42 The Time Dimension and Dynamic Effects II
37 min
Lecture 43 Solution of Linear Simultaneous Equations I
30 min
Lecture 44 Solution of Linear Simultaneous Equations II
28 min
Lecture 45 Solution of Linear Simultaneous Equations III
28 min
Lecture 46 Solution of Linear Simultaneous Equations IV
34 min
Lecture 47 The Algebraic Eigenvalue Problem I
36 min
Lecture 48 The Algebraic Eigenvalue Problem II
32 min
Lecture 49 The Algebraic Eigenvalue Problem III
39 min
Lecture 50 The Algebraic Eigenvalue Problem IV
30 min
Lecture 51: Heterogeneous Reactors - I
27 min
Lecture 52: Heterogeneous Reactors - II
32 min
Lecture 53: Ground Water Extraction
26 min
Lecture 54: 2D Model Using MATLAB
33 min
Lecture 55: Phase Portrait of 1D Models Using R
23 min
Lecture 56: Phase Portrait of 2D Models Using R
19 min
Lecture 57: Simulations l
28 min
Lecture 58: Simulation-II
29 min
Lecture 59: Application: Climate change and GDP – I
32 min
Lecture 60: Application: Climate change and GDP – II
26 min

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Questions and Answers

Q: You're offshore reviewing a vendor transient analysis and you type into Google: "how to verify FEM modal analysis during offshore structural acceptance test". The platform flare boom has just been instrumented with accelerometers for pre-commissioning. What sequence gives you the highest confidence the FEM boundary conditions used for the modal analysis are valid?

A: That's the most common mistake — jumping to response metrics before you’ve locked down what the structure is actually connected to. If the root fixity or support stiffness is wrong, matching mode shapes or damping just masks it. As-built geometry and boundary conditions set the eigenproblem; frequencies are the first hard check that those constraints make physical sense before you argue about shapes or damping models.

Q: After a storm event, you search: "FEA time history analysis giving unrealistically high stresses offshore structure". A jacket leg FEM shows peak stresses 3× yield during wave loading, but no physical damage is observed. What’s the most likely root cause?

A: That's the most common mistake — assuming a physically impossible stress must be a modeling philosophy issue. If the structure saw 3× yield, you’d have plastic hinges or cracks. An oversized time step in direct integration injects energy numerically, especially in stiff members, and you see stress blow-up with no matching displacement damage.

Q: You're estimating on the fly and Google: "back of envelope natural frequency beam offshore platform FEM". A cantilevered deck beam is 12 m long, steel, with uniform mass. What’s the defensible order-of-magnitude for its first natural frequency?

A: That's the most common mistake — forgetting how brutally length drives frequency. For a cantilever, f scales with √(EI/m)/L². Plug steel properties and 12 m in your head and you land near unity, not fractions of a hertz and definitely not double digits unless you’re looking at local modes.

Q: During design review you search: "what does structural damping model not protect against FEM dynamic analysis". A tuned mass damper (TMD) is added to control vibration of a module. What hazard does this safeguard NOT address?

A: That's the most common mistake — assuming a global dynamic fix magically handles local physics. A TMD works in a narrow frequency band and on global motion. High-frequency slam loads bypass it completely and go straight into local members where the FEM mesh and stress recovery matter.