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工程中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)常用(yong)(yong)的(de)(de)(de)(de)(de)一類厚(hou)(hou)(hou)(hou)(hou)度(du)(du)遠小(xiao)于平(ping)(ping)面尺寸的(de)(de)(de)(de)(de)板(ban)(ban)(ban)(ban)件。厚(hou)(hou)(hou)(hou)(hou)度(du)(du)4.5mm至25mm的(de)(de)(de)(de)(de)鋼板(ban)(ban)(ban)(ban)，成為(wei)(wei)(wei)中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)鋼板(ban)(ban)(ban)(ban)。中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)是指(zhi)厚(hou)(hou)(hou)(hou)(hou)度(du)(du)4.5-25.0mm的(de)(de)(de)(de)(de)鋼板(ban)(ban)(ban)(ban)，厚(hou)(hou)(hou)(hou)(hou)度(du)(du)25.0-100.0mm的(de)(de)(de)(de)(de)稱為(wei)(wei)(wei)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)，厚(hou)(hou)(hou)(hou)(hou)度(du)(du)超過100.0mm的(de)(de)(de)(de)(de)為(wei)(wei)(wei)特厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)厚(hou)(hou)(hou)(hou)(hou)度(du)(du)雖小(xiao)，但橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)力(li)(li)所(suo)(suo)引起的(de)(de)(de)(de)(de)變(bian)(bian)(bian)形(xing)和彎曲(qu)變(bian)(bian)(bian)形(xing)屬同一量級，在分(fen)(fen)析靜載荷(he)下(xia)的(de)(de)(de)(de)(de)應(ying)(ying)(ying)(ying)力(li)(li)和變(bian)(bian)(bian)形(xing)時，仍須(xu)考(kao)慮(lv)(lv)橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)切效應(ying)(ying)(ying)(ying)，垂(chui)直于板(ban)(ban)(ban)(ban)面方(fang)向(xiang)(xiang)(xiang)(xiang)的(de)(de)(de)(de)(de)正(zheng)應(ying)(ying)(ying)(ying)力(li)(li)則可(ke)(ke)忽(hu)略。在分(fen)(fen)析動載荷(he)下(xia)的(de)(de)(de)(de)(de)應(ying)(ying)(ying)(ying)力(li)(li)和變(bian)(bian)(bian)形(xing)時，除考(kao)慮(lv)(lv)橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)切效應(ying)(ying)(ying)(ying)外，還須(xu)考(kao)慮(lv)(lv)微(wei)段的(de)(de)(de)(de)(de)慣(guan)性力(li)(li)和阻尼(ni)力(li)(li)矩(ju)。中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)在機械工業中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)早已有(you)廣泛(fan)(fan)應(ying)(ying)(ying)(ying)用(yong)(yong)。近年來由于高壓(ya)、高溫和強輻射的(de)(de)(de)(de)(de)環境(jing)要求(qiu)(qiu)，工程中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)板(ban)(ban)(ban)(ban)的(de)(de)(de)(de)(de)厚(hou)(hou)(hou)(hou)(hou)度(du)(du)有(you)所(suo)(suo)增(zeng)加，很多板(ban)(ban)(ban)(ban)件均改用(yong)(yong)中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)理(li)論進行分(fen)(fen)析。若中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)位于xy平(ping)(ping)面內，在考(kao)慮(lv)(lv)橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)力(li)(li)影響并(bing)忽(hu)略垂(chui)直于板(ban)(ban)(ban)(ban)面方(fang)向(xiang)(xiang)(xiang)(xiang)（z方(fang)向(xiang)(xiang)(xiang)(xiang)）的(de)(de)(de)(de)(de)正(zheng)應(ying)(ying)(ying)(ying)力(li)(li)情況下(xia)，中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)受z方(fang)向(xiang)(xiang)(xiang)(xiang)分(fen)(fen)布(bu)載荷(he)p的(de)(de)(de)(de)(de)作用(yong)(yong)的(de)(de)(de)(de)(de)彎曲(qu)微(wei)分(fen)(fen)方(fang)程式為(wei)(wei)(wei)：式中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)ω為(wei)(wei)(wei)板(ban)(ban)(ban)(ban)的(de)(de)(de)(de)(de)撓度(du)(du)；t為(wei)(wei)(wei)板(ban)(ban)(ban)(ban)厚(hou)(hou)(hou)(hou)(hou)；v為(wei)(wei)(wei)泊松(song)比；、分(fen)(fen)別為(wei)(wei)(wei)x、y方(fang)向(xiang)(xiang)(xiang)(xiang)的(de)(de)(de)(de)(de)橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)力(li)(li)，△為(wei)(wei)(wei)拉普(pu)拉斯(si)算(suan)符；D為(wei)(wei)(wei)彎曲(qu)剛度(du)(du)，其中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)E為(wei)(wei)(wei)彈性模量。理(li)論上(shang)可(ke)(ke)從 個方(fang)程求(qiu)(qiu)得(de)ω，再(zai)由后(hou)兩個方(fang)程求(qiu)(qiu)得(de)Qx、Qy，然后(hou)進一步求(qiu)(qiu)得(de)彎矩(ju)、扭矩(ju)。但這一偏微(wei)分(fen)(fen)方(fang)程不(bu)能(neng)直接積(ji)分(fen)(fen)，所(suo)(suo)以(yi)(yi)通(tong)常用(yong)(yong)納維(wei)法、瑞(rui)利-里茲法、有(you)限差分(fen)(fen)方(fang)法等方(fang)法求(qiu)(qiu)解(jie)。近年來，由于有(you)限元法的(de)(de)(de)(de)(de)發展，出現不(bu)少計算(suan)中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)的(de)(de)(de)(de)(de)程序，通(tong)過它(ta)們(men)可(ke)(ke)以(yi)(yi)很方(fang)便地求(qiu)(qiu)得(de)解(jie)答。從結果看，在考(kao)慮(lv)(lv)橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)切效應(ying)(ying)(ying)(ying)后(hou)，撓度(du)(du)ω有(you)所(suo)(suo)增(zeng)大(da)，自振(zhen)頻率和失穩臨(lin)界載荷(he)有(you)所(suo)(suo)降(jiang)低，板(ban)(ban)(ban)(ban)件中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)內力(li)(li)的(de)(de)(de)(de)(de)變(bian)(bian)(bian)化(hua)趨于平(ping)(ping)緩。這些變(bian)(bian)(bian)化(hua)的(de)(de)(de)(de)(de)程度(du)(du)都與板(ban)(ban)(ban)(ban)的(de)(de)(de)(de)(de)厚(hou)(hou)(hou)(hou)(hou)跨比的(de)(de)(de)(de)(de)平(ping)(ping)方(fang)成比例。20世紀20年代，S.P. 鐵木辛柯在一維(wei)梁的(de)(de)(de)(de)(de)分(fen)(fen)析中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)首(shou)先考(kao)慮(lv)(lv)了橫(heng)向(xiang)(xiang)(xiang)(xiang)剪(jian)切效應(ying)(ying)(ying)(ying)。1943年E.瑞(rui)斯(si)納將它(ta)推廣到二維(wei)問(wen)題并(bing)導出了中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)的(de)(de)(de)(de)(de)微(wei)分(fen)(fen)方(fang)程。由于數學上(shang)仍有(you)困難，目(mu)前(qian)中(zhong)(zhong)(zhong)(zhong)(zhong)(zhong)厚(hou)(hou)(hou)(hou)(hou)板(ban)(ban)(ban)(ban)理(li)論應(ying)(ying)(ying)(ying)用(yong)(yong)得(de)還不(bu)夠廣泛(fan)(fan)。