Jiang Ke. Plastic Limit Analysis of Plane Stress Problems by Truss Element. Preprint at https://doi.org/10.2139/ssrn.4476517 , 2023.
The Most Beautiful Animation of Plasticity in History
(1) https://www.bilibili.com/video/BV1ns4y1F7t1/?spm_id_from=333.999.0.0
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
The new model of truss element is based on the same stress-strain curves of tension, compression, and shear with the hexahedron element under the equivalent external force. Comparing and analyzing a simply supported elastoplastic concrete beam with initial cracks by using the new element method and the finite element method, it can be found that the load-displacement curve, the load-crack opening displacement curve, the contour of the displacement under the various loads, and the distribution of the horizontal normal stress under the maximum load are all in good agreement.
For the plane stress problem and the spatial problem of the elasto-plastic analysis of concrete, a new truss element model is presented by using the deformations under the equivalent external forces are the same. Some examples is given, which is in good agreement with the calculation results of the solid element.
(Note: The model in this article is the world's top concrete model, much better than the concrete model provided by Ansys itself.)
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
The plane stress problems have solved by using a new orthotropic element model, compared with the finite element method, it can be found that the results of the two methods are in good agreement.
Supplemental Videos:
(1) https://www.bilibili.com/video/BV1yd4y167i6/?spm_id_from=333.999.0.0
(2) https://www.bilibili.com/video/BV1CV4y1M7y6/?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).