Force-Based Higher-Order Shear Beam Element Model for FG Sandwich Beams Analysis

Основные понятия

Introducing a force-based higher-order shear beam element model with rational shear stress distribution for accurate analyses of functionally graded sandwich beams.

Аннотация

This study presents a novel approach to modeling functionally graded sandwich beams using a force-based higher-order shear beam element model. Unlike conventional methods, this model considers stress resultants as unknown fields, leading to more accurate solutions. By incorporating differential equilibrium equations on stresses, the model accurately depicts transverse shear stress distributions. The modified shear stiffness derived from rational shear stress enhances the precision of the proposed beam element. Various studies have validated the effectiveness of higher-order shear beam models in predicting strain and stress distributions accurately. The proposed model addresses limitations in existing models by ensuring high-precision displacement solutions and accurate stress distributions.

Статистика

The Young’s modulus along the thickness is given by E(y) = mE + cE - V(y).
Constitutive relation: E(y) / G(y) = 2 / (1 + v).
Transverse normal strain and transverse normal stress are ignored.
Three types of FG beams considered: isotropic FG beams (Type A), sandwich beams with FG faces and homogeneous core (Type B), sandwich beams with FG core and homogeneous faces (Type C).
Rational distribution of transverse shear stress obtained through differential equilibrium equation on stresses.

Цитаты

"The closed-form solutions of these stress resultants are analytically determined based on the differential equilibrium equations of the higher-order shear beam."
"A modified shear stiffness, which takes into account rational shear stress, is derived and incorporated into the proposed beam element."
"Numerical examples underscore the accuracy and efficacy of the proposed higher-order beam element model in the static analysis of functionally graded sandwich beams."

Ключевые выводы из

A force-based higher-order shear beam element model with rational shear stress distribution for accurate analyses of FG sandwich beams

by Wenxiong Li,... в arxiv.org 03-19-2024

https://arxiv.org/pdf/2312.14367.pdf

Дополнительные вопросы

How can this force-based higher-order shear beam element model be applied to other composite materials beyond functionally graded structures

The force-based higher-order shear beam element model can be applied to other composite materials beyond functionally graded structures by adjusting the material properties and distribution equations accordingly. For different types of composite materials, such as laminates or hybrid composites, the Young's modulus and shear modulus distributions along the thickness would need to be defined based on the specific characteristics of those materials. By incorporating these material properties into the constitutive relations and stress equilibrium equations, the model can accurately analyze the behavior of beams made from various composite materials.

What are potential drawbacks or limitations of using rational shear stress distribution in finite element analysis compared to traditional methods

One potential drawback of using rational shear stress distribution in finite element analysis compared to traditional methods is that it may introduce additional complexity to the modeling process. Rational shear stress distribution requires a more detailed understanding of how transverse shear stresses vary through the thickness of a beam, which could lead to increased computational effort and time during analysis. Additionally, accurately determining rational shear stress distributions may require more advanced analytical techniques or experimental data compared to traditional methods that rely on simpler assumptions.

How might advancements in exact finite element methods impact the development and application of this novel modeling approach

Advancements in exact finite element methods can significantly impact the development and application of this novel modeling approach by providing a framework for constructing high-precision finite element models with analytical internal force fields. The use of closed-form solutions derived from differential equilibrium equations allows for more accurate predictions without relying solely on numerical discretization. This approach enhances both accuracy and efficiency in analyzing complex structures like functionally graded sandwich beams. As exact finite element methods continue to evolve, they are likely to further improve the precision and reliability of force-based higher-order shear beam element models for a wide range of applications beyond FG sandwich beams.