1, Mathematical Complexity: Elasticity itself is a discipline based on mathematical and physical principles. It involves a wide range of mathematical concepts and skills, such as calculus, partial differential equations, vector analysis and so on. These mathematical tools and deduction processes may be relatively complex and abstract for learners, and they need a strong mathematical foundation and logical thinking ability.
2. Abstract concept: Elasticity involves some abstract concepts and theories, such as stress, deformation and strain energy. These concepts themselves are not intuitive and need to be understood abstractly. It may be a challenge for beginners to build a bridge from concrete physical phenomena to abstract mathematical models.
3. Linear loss: In the real world, the mechanical properties of many materials do not strictly conform to the hypothesis of elasticity theory. For example, when the stress reaches a certain range, the material may undergo plastic deformation or failure, which cannot be effectively described by the elastic theory. Therefore, in order to describe the behavior of materials more accurately, it is necessary to introduce more complex nonlinear mechanical theory or material model.
4. Complex boundary conditions: In practical problems, we often face various complex boundary conditions, such as uneven load, friction and contact. Dealing with these boundary conditions requires complex mathematical modeling and solving skills, which may be a challenge for learners.