In addition to the research and design of China spacecraft, Hu Haichang has published more than 100 papers, covering the fields of elasticity, plasticity, fluid mechanics, balance, stability and vibration of structural mechanics. There are also seven books written and translated. His research work is very creative, especially his outstanding achievement in generalized variational principle, which is an important contribution to mechanics and has a great influence in the international mechanical field. Because most mechanical problems in engineering are difficult to get exact solutions, it has become a long-term discussion topic in mechanics to find their simple, feasible and practical approximate solutions.
Before 1950s, various important approximate solutions can be roughly divided into three categories: the first category is to make some simplified assumptions according to the mechanical background and establish the engineering practical structure theory. From the point of view of solid mechanics, most of these approximate theories accurately satisfy the continuity conditions and equilibrium conditions and approximately satisfy the constitutive relationship, such as beam, plate and shell theory. The second kind is to find the approximate solution by Ritz method according to the principle of minimum potential energy. Although they can meet the requirements of continuity condition and constitutive relation accurately, they can only meet the equilibrium condition approximately. The third kind is to find the approximate solution by Ritz method according to the principle of minimum complementary energy. Although they can accurately satisfy the equilibrium condition and constitutive relation, they only approximately satisfy the continuous condition.
When he was still in college, Hu Haichang began to explore this topic under the guidance of Qian Lingxi, trying to find a method, not demanding the exact satisfaction of any equation, but leaving the problem of which equations can be accurately satisfied and which equations can be approximately satisfied to the problem solver to make a choice according to the nature of the problem. In 1950, E.H. Reissner put forward the generalized variational principle of two kinds of variables in elasticity, which showed the possibility of satisfying different mechanical properties equations approximately at the same time in the energy method. Then, in 1954, Hu Haichang published "On Generalized Variational Principles in Elastic Mechanics and Consistent Mechanics" in the Journal of Physics, in which generalized variational principles of three kinds of variables were put forward. In this variational principle, displacement, strain and stress are all regarded as functions of independent variables, and all equations do not need to be satisfied accurately. This is an unconditional variational principle, which provides an explanation of the viewpoint of energy method for the previous engineering actual structure theory and an unprecedented flexible theoretical basis for studying various approximate solutions.
After the publication of this paper, in 1950s and 1960s, there was an upsurge of studying variational principles in China. On the one hand, the approximate solution is obtained by Ritz method according to the generalized variational principle, which is a pioneering work in the world, five years earlier than the similar work abroad. On the other hand, the generalized variational principles of plate, shell, vibration and stability have been put forward one after another, and they are also in a leading position in the world.
1964, American counterparts took the lead in calling Hu Haichang's variational principle Hu's principle (Japanese Koichiro proposed the same variational principle as American Hu's in 1955). Around 1970, it has been pointed out that the generalized variational principle is a solid theoretical basis for establishing various approximate solutions including finite element method. In this way, there has also been an upsurge of studying and using variational principles abroad, especially to demonstrate existing and establish new finite element methods according to generalized variational principles. Since then, Hu's principle has been recognized by colleagues in the United States, Japan, the Soviet Union, Britain, France, Germany and Italy, and has been introduced and cited in many monographs and papers on elasticity, shell theory and finite element method. It is rare for a domestic mechanical research result to cause such a strong response abroad.
1982 the research achievement of five-position mechanics led by Hu Haichang won the second prize of the National Natural Science Award, and his monograph Variational Principles of Elastic Mechanics and Its Application won the National Excellent Science and Technology Book Award.
A new boundary integral equation is established.
Since the 1960s, boundary integral equation and boundary element method have gradually emerged, and now they are listed as the four major methods in computational mechanics along with finite element method, weighted residual method and difference method. Mathematically, the second kind of integral equation is convenient for numerical solution, while the first kind of integral equation is poor. In the past, what kind of boundary integral equation belongs to depends on the nature of boundary conditions in the problem, not on the will of the problem solver.
In 1986, Hu Haichang derived a new mechanical boundary integral equation from the conservation integral.
The old and new types of boundary integral equations are just complementary, that is, on the same boundary of the same problem, if the old method gives the first type (second type) integral equation, then the new method gives the second type (first type) integral equation. In this way, by combining the old and new boundary integral equations, the second or first type integral equations can be obtained on all boundaries according to the wishes of the solver. This discovery makes the boundary integral equation and boundary element method more promising. Recently, this idea has been applied to solving mixed boundary value problems of plane second-order elliptic equations and stress analysis of elastic bodies with cracks. Numerical examples show that it does have the expected advantages. At present, this work is being carried out step by step.
Transverse isotropic elastomer
(Some important solutions of transversely isotropic elastic body space problems are established)
The international research on anisotropic elasticity began as early as19th century. Before 1953, people have obtained many solutions to the plane problem, torsion problem, bending problem and axisymmetric deformation problem of transversely isotropic bodies. Although it is a spatial problem in mechanics, it is a two-dimensional problem in mathematics. Some solutions to real three-dimensional space problems were not found by Hu Haichang until 1953.
Hu Haichang used two displacement functions to represent the displacement of transversely isotropic body, which greatly simplified the equation to be solved. Through the displacement function, a series of solutions of real three-dimensional space problems are obtained, some of which are of great significance in the application of foundation and foundation analysis in civil engineering. Hu Haichang's work in this field has attracted the attention of foreign counterparts such as the Soviet Union and the United States, and has been quoted and introduced in his papers and monographs.
Hu Haichang and his colleagues also used the above methods to solve the problems of spherical isotropic elastic body, medium and thick plates (including sandwich plates), thin shells and medium thick shells, prestressed cylindrical shells and so on, and achieved fruitful results.
1956, his research achievement "The Spatial Problem of Transversely Isotropic Body Elasticity" won the third prize of Natural Science Award of China Academy of Sciences.
In addition, Hu Haichang also made important discoveries in the study of large deflection of elastic thin plate shells. In the past, the large deflection problem of elastic thin plate shells was usually solved by small parameter method. In 1954, Hu Haichang found that the results obtained with different small parameters can be transformed into each other in the formula, but if the finite term is taken, the approximation degree of the numerical results is very different. So he first put forward the problem of choosing better small parameters, and suggested using generalized displacement as small parameters first. The selection of small parameters has been studied until the 1980s.
Promote the research and application of vibration theory and technology.
In 1980s, Hu Haichang actively advocated the transition from static design to dynamic design, promoted the research and application of vibration theory and technology, established the China Society of Vibration Engineering, and founded the academic journal of vibration research. He also attached great importance to the study of vibration theory and made many important achievements. For example, the universality of vibration in structural theory is demonstrated by the combination of mechanics and functional theory; The small parameter method and local correction method are applied to the natural vibration of multi-degree-of-freedom structures. The inclusion theorem and counting theorem of eigenvalue are improved and developed.
1987 cooperated with the collaborator * * * to study the positive definiteness and compactness of two kinds of operators in linear elastic structure theory, and won the second prize of scientific and technological progress of the State Education Commission.
(Author: Wang Dajun)