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Energy Approaches
Published in Cameron Coates, Valmiki Sooklal, Modern Applied Fracture Mechanics, 2022
Cameron Coates, Valmiki Sooklal
If we examine the stress–strain curve shown in Figure 3.8, the shaded region is the area under the curve and represents the strain energy density u, which is also a measure of the fracture toughness of the material. It is useful to note the significantly larger area and thus fracture toughness for the ductile material shown, compared to the brittle under similar loading. The strain energy density has units of J/m3, and represents the energy required to deform the material. The total strain energy in the bar can be expressed as U=∫0εσdε
Energy Methods and Stability
Published in Ansel C. Ugural, Mechanical Engineering Design, 2022
As pointed out in Section 1.4, instead of the equilibrium methods, displacements and forces can be ascertained through the use of energy methods. The latter are based on the concept of strain energy, which is of fundamental importance in analysis and design. The application of energy techniques is effective in cases involving members of variable cross-sections and problems dealing with elastic stability, trusses, and frames. In particular, strain energy approaches can greatly ease the chore of obtaining the displacement of members under combined loading.
Energy Methods and Stability
Published in Ansel C. Ugural, Youngjin Chung, Errol A. Ugural, Mechanical Engineering Design, 2020
Ansel C. Ugural, Youngjin Chung, Errol A. Ugural
As pointed out in Section 1.4, instead of the equilibrium methods, displacements and forces can be ascertained through the use of energy methods. The latter are based on the concept of strain energy, which is of fundamental importance in analysis and design. The application of energy techniques is effective in cases involving members of variable cross-sections and problems dealing with elastic stability, trusses, and frames. In particular, strain energy approaches can greatly ease the chore of obtaining the displacement of members under combined loading.
Quantitative Evaluation Method of Structural Safety for the Great Wall Hollow Defensive Forts under Gravity Loads
Published in International Journal of Architectural Heritage, 2022
Haoyu Wang, Qing Chun, Chengwen Zhang, Pan Li, Dongqing Li, Fei Zhai
The importance calculation of structural components is a method based on the change of structural strain energy (Ye et al. 2010). Strain energy is the potential energy stored in the object as strain and stress. For a conservative member structural system, the total strain energy is the sum of the strain energy of all members in the system, converted from the work done by the external load. The component importance index is defined as the change rate of the component change to the generalized stiffness (structural strain energy) of the structure, and the simplified expression is as follows:
Application research of a structural topology optimization method based on a bionic principle
Published in Engineering Optimization, 2021
Yuhai Zhong, Huashan Feng, Runxiao Wang
The energy stored in materials when loads are applied is called the strain energy. Since it is scalar, strain energy is not directional. Applying the strain energy per unit mass as the mechanical stimulus can simplify the algorithm. The mechanical stimulus is defined as: where is the SED, which can be calculated by ; and and are stress components and strain components, respectively.
FEA Based Design and Stability Study of Electroless Ni-P Coating Plated over a Stepped Shaft under Thermal Load
Published in Australian Journal of Mechanical Engineering, 2023
Tarik Hassan, Subhasish Sarkar, Tapendu Mandal, Nitesh Mondal, Gautam Majumdar
A separate study is performed to analyse results along a straight line in the model which is a very helpful tool to check the variation of data along that line. The values of equivalent stress () and strain energy (SE) are evaluated along the four different paths as discussed earlier, and the data are plotted against the radial distance with respect to the axis of the shaft as shown in Figures 9 and 10, respectively. The prime objective of finding the data along a path is to calculate the change in the values of and SE between the coating and the shaft. This change may be a helpful measure to predict the design stability of the coating over the surface of the substrate. From the atomic scale to a macro-scale substance, everything is connected to energy in various ways. It is also an important scientific fact that the energy level is indirectly proportional to the level of stability. Therefore, every object in this universe is trying to minimise its energy to gain better stability, like the electron in the outer orbit of an atom is very unstable and mainly responsible for chemical bonding because of its higher energy state while the reverse happens to the inner orbit electron due to lower energy level (Xu et al. 2018; Rohrlich 1960; Saville et al. 2011). In the case of elastic material, strain energy is one form of potential energy which is generated in a deformed body due to the generation of stress. The body which has higher SE or induced stress is capable of performing higher elastic work, making itself less stable and more prone to cause failure. Han et al. (2021) used the advanced concept of strain and resonance energy to analyse the stability and performance of explosives. Similarly, the ligand strain energy of the metal-organic framework (MOF) is compared with its stability by Shustova, Cozzolino, and Dinca (2012). The main objective here is to justify that the strain energy is an important determining parameter for the design stability of an elastic body.