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Beams with Symmetric Loadings

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...

Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

Method of Sections

Method of Sections

Consider a truss structure, as shown in the figure.

Method of Joints: Problem Solving I

Method of Joints: Problem Solving I

The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC,...

Internal Loadings in Structural Members: Problem Solving

Internal Loadings in Structural Members: Problem Solving

When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
To illustrate this, let's consider a beam OC of 5 kN, inclined at an angle of 53.13° with the horizontal and supported at both ends. Determine the internal...

Method of Joints: Problem Solving II

Method of Joints: Problem Solving II

Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.

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Related Experiment Video

Updated: Feb 23, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Published on: July 25, 2025

Weld inspection by focused adjoint method.

Khaled Metwally¹, Emma Lubeigt², Sandrine Rakotonarivo¹

¹Aix-Marseille Université, CNRS, Centrale Marseille, LMA, Marseille, France.

|September 3, 2017

Summary

This study introduces a novel non-destructive ultrasonic method for weld evaluation. It efficiently detects weld anomalies using time reversal and topological imaging for enhanced accuracy.

Keywords:

Adjoint method Finite element modeling Topological energy Wave focusing Weld inspection

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Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

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Area of Science:

Materials Science
Non-Destructive Testing
Ultrasonic Wave Propagation

Background:

Weld integrity is crucial for structural safety.
Current non-destructive evaluation (NDE) methods face challenges with heterogeneous materials.
Accurate defect detection in welds remains a significant concern.

Purpose of the Study:

To develop an advanced methodology for non-destructive ultrasonic evaluation of welds.
To enhance the efficiency and accuracy of anomaly detection in welds.
To enable precise imaging of defects in anisotropic media.

Main Methods:

Utilizes probing, residue back-focusing, and topological energy calculation.
Employs an enhanced (focused) adjoint method for wave analysis.
Combines time reversal for distortion compensation and topological imaging for defect localization.

Main Results:

Demonstrates efficient detection of anomalies in welds.
Highlights the synergistic effect of combining time reversal and topological imaging.
Successfully compensates for wave distortions in heterogeneous media.

Conclusions:

The proposed method offers a highly efficient approach for weld anomaly detection.
This technique paves the way for matched-insonification imaging in anisotropic materials.
The methodology advances non-destructive ultrasonic evaluation capabilities for critical structures.