One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in...

Area of Science:

• Solid Mechanics
• Materials Science
• Structural Engineering

Background:

• Functionally graded materials (FGMs) exhibit spatially varying properties.
• Bimodular materials possess different elastic moduli in tension and compression.
• Combining FGMs with bimodular characteristics presents unique mechanical challenges.

Purpose of the Study:

• To develop 1D and 2D mechanical models for bimodular FG beams.
• To obtain analytical solutions for beams under pure and lateral-force bending.
• To analyze the impact of varying tensile and compressive moduli on stress distribution.

Main Methods:

• Establishment of one-dimensional (1D) and two-dimensional (2D) mechanical models.
• Utilizing an exponential expression for the material's grade function.
• Derivation of analytical solutions for bending scenarios and verification of model regression.

Main Results:

• Analytical solutions derived for bimodular FG beams under various bending conditions.
• Verification of the 2D model's regression to the 1D model.
• Demonstration that maximum tensile and compressive stresses may not be at the beam's extremities.

Conclusions:

• The bimodular functionally graded effect significantly alters stress distribution.
• The location of maximum bending stress is dependent on material properties and loading.
• The study provides a method to determine the precise location of maximum stress.