What is the matter of the kirchhoff plate theory?
Best insight from top research papers
The Kirchhoff plate theory is a mathematical model used to describe the behavior of thin plates. It provides a framework for analyzing the bending and deformation of these plates. The theory takes into account various factors such as strain, strain gradient, rotation gradient, and couple stress. It also considers the size effect of thin plates, which is determined by geometric dimensions and length-scale parameters. The theory can be modified to suit different conditions and can be reduced to other plate models such as the classical Kirchhoff-Love plate model and the couple stress thin plate model. The governing equations and boundary conditions for the Kirchhoff plate theory can be obtained using principles such as the principle of minimum potential energy and Hamilton's extended principle.
Answers from top 3 papers
More filters
| Papers (3) | Insight |
|---|---|
21 Mar 2019 1 Citations | The paper does not explicitly mention the matter of the Kirchhoff plate theory. |
| The paper discusses a modified gradient elastic Kirchhoff-Love plate model, which describes the bending deformation of thin plates more flexibly by introducing couple stress and modifying the classical bending stiffness. The specific modified classical boundary conditions and non-classical higher-order boundary conditions for the bending boundary value problems are derived. However, the paper does not explicitly mention the matter of the Kirchhoff plate theory. | |
Open access•Posted Content | The paper discusses the derivation of a linearized Kirchhoff model for plates with incompatible prestrain as their thickness tends to zero. |
Related Questions
What is my plate?5 answers"My Plate" is a concept introduced to promote healthy eating habits by providing guidelines on food proportions for different food groups like fruits, vegetables, cereals, protein, and dairy. It aims to assist individuals in achieving a balanced diet. The concept of "My Plate" is part of a broader effort to address unhealthy food trends and improve nutrition, especially among children and adolescents. While the universal adoption of "My Plate" may not be feasible in all regions due to cultural and economic factors, localized adaptations have been attempted to cater to specific populations, such as in the coastal region of Karnataka, India. Overall, "My Plate" serves as a visual tool to guide individuals towards making healthier food choices and maintaining a well-rounded diet.
What is Blasius theory on a flat plate with zero incidence?4 answersBlasius theory describes the flow of an incompressible fluid over a flat plate with zero incidence. It is based on the Blasius equation, which is a third-order ordinary differential equation that represents the problem. The Blasius equation can be recast into a system of nonlinear algebraic equations using B-spline functions. Numerical solutions have been found to be in good agreement with other published methods. The Blasius equation is also used to study laminar boundary layers, which are the distance from the surface to a particular point perpendicular to the flow direction where the flow velocity has retained 99% of the free stream velocity. The properties of the laminar boundary layer, such as velocity profile, boundary layer thickness, displacement thickness, momentum thickness, shape factor, wall shear stress, friction coefficient, and drag coefficient, can be studied using exact solutions of the Blasius equation and finite volume solutions of the Navier-Stokes equations.
Why is relevant to study stiffened plates?3 answersStudying stiffened plates is relevant for several reasons. Firstly, the addition of stiffeners to plates can significantly increase their strength. This is important in various engineering applications where higher strength is required. Secondly, understanding the behavior of stiffened plates under different loading conditions is crucial for assessing their ultimate strength. This knowledge can help in designing and optimizing structures to ensure their safety and reliability. Additionally, studying the dynamic characteristics of stiffened plates is essential for examining vibration and noise in structures such as steel box girders. This information can be used to reduce responses due to vibrations and noise, leading to improved performance and comfort. Finally, investigating the forced vibration analysis of stiffened plates can provide insights into their behavior and help in optimizing their design.
How can classical plate theory be used to model the behavior of plates?4 answersClassical plate theory can be used to model the behavior of plates by considering the plate as a two-dimensional structure and using a single displacement function for the complete formulation of the plate. This theory does not require a shear correction coefficient and can be used to solve plate problems in a similar manner as classical plate theory. By using the Kirchhoff-Love model and considering the orthotropic nature of the plate material, the bending energy and equilibrium equation of the plate can be obtained. The kinetic energy of the plate can also be determined, and combined with the bending energy, it gives the complete Lagrangian and equation of motion for the plate. This approach allows for a better description of rectangular plates with different behaviors in different directions.
What is the buckling of plates?5 answersThe buckling of plates refers to the behavior of plates when they undergo bending in two planes and fail to resist further load. It is a sudden failure mode that can occur either before or after material yielding. Elastic buckling occurs when buckling happens before material yielding, while plastic buckling occurs after material yielding. Plate buckling is usually referred to as local buckling and involves the bending of plates in two planes, making it more complex than the buckling of framed members. The classical theory of plate buckling emerges from dimension reduction procedures applied to incremental elasticity theory, where plate buckling theory is the leading-order-in-thickness model when pre-stress scales appropriately with respect to thickness. The buckling analysis of plates involves solving governing equations for different loading conditions and boundary conditions, and can be solved analytically for certain cases.
Benefits of plate tectonics theory?1 answersThe theory of plate tectonics provides a robust framework to describe and predict the behavior of Earth's lithosphere. It allows us to understand the geological characteristics of other rocky bodies in our solar system and beyond. Plate tectonics explains the vertical and horizontal movements of the lithosphere, leading to mountain building, the opening and closing of oceans, and other geological processes. Additionally, plate tectonics helps in explaining the distribution and genesis of known mineral deposits, revealing new prospects for energy and mineral resources. Furthermore, plate tectonics plays a significant role in defining the habitability of terrestrial planets, as it facilitates the cycling of material between near-surface and mantle reservoirs, heat transport, and the formation of continental crust. Overall, the benefits of plate tectonics theory include a better understanding of Earth's geodynamic evolution, the prediction of geological processes, and the exploration of mineral and energy resources.