Jiang Ke's blog

Based on a new element model of solid body, the plastic limit analysis of plate is carried out. The new element model is a truss composed of 24 bars. Taking the simply supported square plate and rectangular plate under uniform load as an example, by comparing the new element method with the classical plastic limit analysis theory, it can be found that the limit load and the distribution of plastic zone obtained by the two methods are in good agreement.

This is a beautiful, unparalleled elastoplastic model for plastic materials.

Based on the equivalent stress and deformation of regular hexahedron microelement and truss element, a new truss element model is presented. It can be used to solve the elasto-plastic plane stress problem and spatial problem of steel. Through a large number of examples, the new element model can be found to have good accuracy.

The plastic limit of beams and frames have analyzed by using a new truss element model of solid bodies, compared with the plastic limit analysis method, it can be found that the limit load of the two methods are in good agreement.

Supplemental Videos:

(1) https://www.bilibili.com/video/BV1Yt4y1A7a1/?spm_id_from=333.999.0.0

(2) https://www.bilibili.com/video/BV1vg411U7Dv/?spm_id_from=333.999.0.0

For orthotropic plane strain problems, the various existing calculation methods are very complex. The orthotropic plane strain problem with cracks have solved by using a new element model, and compared with the finite element method, it can be found that the displacements and the stresses of the two methods are in good agreement.

Supplemental Videos:

(1) https://www.bilibili.com/video/BV1QW4y1e7YQ/?spm_id_from=333.999.0.0

      Jiang Ke. Orthotropic metamaterials with freely tailorable elastic constants. Preprint at https://doi.org/10.48550/arXiv.2205.14176 (2022).  

      It has great application value in the fields of mechanical metamaterials, elastic wave metamaterials, acoustic metamaterials, and seismic metamaterials, and has opened up a broad road for realizing the dream of controlling elastic waves, acoustic waves and vibrations.

The solution of linearly elastic and orthotropic solid bodies is very complicated, thus a new element model for solving linearly elastic and orthotropic bodies is presented by using the generalized Hooke's law and the superposition principle. This new model is a simple truss consisting of some bars, and then the solution of orthotropic body becomes simple. Furthermore, this new model reveals the physical mechanism of a solid body under the action of applied forces.

Keywords: Elasticity, new model, orthotropic body, truss, generalized Hooke's law

Based on the generalized Hooke's law and the superposition principle, a new element model of linearly elastic and orthotropic solid bodies is presented. Furthermore, the paper provides a new method for analyzing solid bodies. This new element is a simple truss, and a solid body is considered to consist of many such truss elements, then the solid body becomes a truss structure. Thus the internal forces and displacements of the solid body can be obtained by calculating this truss structure.

Keywords: solid body, element model, Elasticity, Hooke's law, truss element

 Jiang Ke. A new method for solving solid structures. COMPUTATIONAL MECHANICS: Proceedings of International Symposium on Computational Mechanics (ISCM 2007), July 30-August 1, 2007, Beijing,China. Tsinghua University Press & Springer.