Single-Course English 5 ECTS

# Stiffened plates and sandwich constructions

## Overall Course Objectives

With a mathematical and physical basis, to analyse the strength and stability of different types of technically important lightweight plate structures, consisting of steel, aluminum and advanced sandwich composite materials, and to use this analysis expertise to analyze and dimension plate elements in weight critical constructions such as aircrafts, ships, bridges, offshore structures, automotive and space vehicles.

Learning Objectives

• Account for the assumptions for first and higher order plate theories for both unstiffened, stiffened and layered sandwich plates.
• Formulate relevant boundary conditions for plate fields in large plate structures.
• Perform theoretical stress and deformation analyses of unstiffened and stiffened plate structures with a rectangular geometry by use of Navier’s method and Rayleigh-Ritz’s method (the energy method).
• Perform theoretical stress and deformation analyses of sandwich beams with shear deformations.
• Perform theoretical stress and deformation analyses of layered sandwich plates with an outset in classical lamination theory and basic sandwich theory with shear deformations.
• Perform theoretical stability analysis of rectangular unstiffened, stiffened and layered sandwich plates.
• Account for ultimate strength of rectangular, laterally loaded unstiffened and stiffened plate structures.
• Account for the carrying capacity of rectangular stiffened plate structures exposed to in-plane compression loading using the effective width theory.
• Calculate progressive failure of rectangular and laterally loaded sandwich plates using failure criteria for composite materials.
• Use a commercial FEM program to analyze and design both unstiffened as well as stiffened plate structures consisting of either metallic or typical sandwich composite materials.
• Compare analytical, numerical and experimentally achieved results for a given plate structure and evaluate the quality of the results.
• Write a technical report containing analysis including the above mentioned points applied on a practical design example from an aircraft, ship, bridge, offshore structure, automotive or space vehicle.

Course Content

The main focus of the course is the application of basic analytical methods (based on differential equations, energy conservation and failure criteria) for practical weight critical plate structures from a span of application areas and consisting of metallic as well as advanced sandwich composite materials, and thus obtain a regious physical understanding for the mechanical behavior and practical application of plate structures.

1) Unstiffened and stiffened plates: Differential equations, stiffness behavior of stiffened plate panels, stress calculation, boundary conditions, analysis methods (Navier and Rayleigh-Ritz methods). Plates with large deformations.

2) Layered sandwich beams and plates: Differential equations, stiffness properties and their connection to Classic Lamination Theory, stress calculation, basic sandwich theory with shear deformations and first order sandwich beam and plate theories and their analysis methods.

3) Stability of plates: Analytical buckling analysis methods, energy method, stiffened plates, buckling of layered sandwich plates and the influence of imperfections.

4) Ultimate strength and progressive failure: Yield line theory, ultimate strength for metallic plates and progressive failure analysis of layered sandwich plates.

5) Design principles and practical application of analytical solutions and FEM analysis for plate structures within typical weight critical constructions such as aircrafts, ships, bridges, offshore structures, automotive and space vehicles.

6) Experimental methods for plate structures consisting of metallic as well as composite materials.

Recommended prerequisites

41516/41812/11305/41958, and knowledge of MatLab or similar.

Teaching Method

Lectures and project work in groups of max. 2 students.
Throughout the course students will work with two practical design cases, which will be supported by the lectures.

Faculty

Remarks

The course is relevant for both mechanical and civil engineering students, as well as neighboring fields such as wind energy, space technology etc., by supporing these fields with suitable application examples and project assignments.

See course in the course database.

## Registration

Language English 13 weeks DTU Lyngby Campus 41517 Candidate Week 5 Week 19 Thurs 8-12
Price 7.500,00 DKK