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双模量材料是典型的拉压弹性模量不同的材料,在均匀外载荷作用下,双模量面板泡沫铝芯圆形层合板相当于三种不同材料组成的层合板。采用弹性理论建立了双模量面板泡沫铝芯圆形层合板在均布载荷作用下的静力平衡方程,利用该静力平衡方程确定了层合板的中性面位置。在此基础上建立了双模量面板泡沫铝芯圆形层合板的大挠度弯曲微分方程组,求得了层合板中心挠度与均布载荷的关系式。该方法计算结果与有限元计算结果的最大误差仅为3.8%,这说明该方法是可靠的。算例分析表明不考虑面板拉压弹性模量相异时其计算结果与实际情况相差较大,超过了工程上所允许的计算误差5%。所以,在计算双模量面板泡沫铝芯圆形层合板的非线性弯曲时,不宜采用相同弹性模量弹性理论,而应该采用拉压弹性模量不同的弹性理论。
The biaxial material is a typical material with different tensile elastic modulus. Under the uniform external load, the bimodular foam aluminum core circular laminated plate is equivalent to the laminate of three different materials. Based on the elastic theory, the static equilibrium equation of the bimodulus foam aluminum core circular laminated plate under uniform load is established, and the neutral plane position of the laminated plate is determined by the static equilibrium equation. On this basis, the large deflection bending differential equations of the bimodulus foam aluminum circular laminated plates are established, and the relationship between the center deflection and the uniform load of the laminated plates is obtained. The maximum error between the calculated results and the finite element results is only 3.8%, which shows that the method is reliable. The case study shows that the calculation results differ from the actual situation when the elastic modulus of tension and compression of the panel is different, which exceeds 5% of the allowable calculation error in engineering. Therefore, it is not appropriate to use the same theory of elasticity of elasticity when calculating the nonlinear bending of a circular die-cast aluminum foam panel with a dual-modulus panel. Instead, the elastic theory of tension-compression elastic modulus should be adopted.