Giá trị gần đúng của các tải quan trọng thu được theo phương pháp năng lượng luôn luôn lớn hơn các giá trị chính xác. Giải thích nằm trong thực tế là một hình dạng lệch giả ngụ ý việc áp dụng các hạn chế để buộc cột để có một hình dạng nhân tạo. Điều này, như chúng ta đã thấy, có tác dụng cứng cột với một sự gia tăng kết quả tải trọng. | Buckling of thin plates 169 from which cR 17 2 2 This value of critical load compares with the exact value see Table of Tĩ2 El 4 2 I2 the error in this case is seen to be extremely small. Approximate values of critical load obtained by the energy method are always greater than the correct values. The explanation lies in the fact that an assumed deflected shape implies the application of constraints in order to force the column to take up an artificial shape. This as we have seen has the effect of stiffening the column with a consequent increase in critical load. It will be observed that the solution for the above example may be obtained by simply equating the increase in internal energy Í7 to the work done by the external critical load - K . This is always the case when the assumed deflected shape contains a single unknown coefficient such as vn in the above example. Buckling of thin plates A thin plate may buckle in a variety of modes depending upon its dimensions the loading and the method of support. Usually however buckling loads are much lower than those likely to cause failure in the material of the plate. The simplest form of buckling arises when compressive loads are applied to simply supported opposite edges and the unloaded edges are free as shown in Fig. . A thin plate in this configuration behaves in exactly the same way as a pin-ended column so that the critical load is that predicted by the Euler theory. Once this critical load is reached the plate is incapable of supporting any further load. This is not the case however when the unloaded edges are supported against displacement out of the VJ plane. Buckling for such plates takes the form of a bulging displacement of the central region of the plate while the parts adjacent to the supported edges remain straight. These parts enable the plate to resist higher loads an important factor in aircraft design. At this stage we are not concerned with this post-buckling behaviour .